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ABSTRACT
MORERA, FRANCISCO. Lateral Flange Bending in Heavily Skewed Steel Bridges. (Under
the direction of Dr. Emmett A. Sumner)
The problem related to lateral flange bending of steel plate skewed girders during the non
composite phase of construction can be simply stated as a consequence of the significant
support skew, typical staggered crossframes along the span in between adjacent girders,
differential deflections commonly present on skewed bridges, out of plumb condition
associated with girder camber and imperfections, and the force transfer mechanism due to the
overhang falsework.
Two different simple span steel I-girder skewed bridges were monitored during the non
composite phase of the construction process in order to study the effect of Lateral Flange
Bending (LFB) on both displacements and stresses. Using ANSYS V 11.0 as the Finite
Element software, numerical models of the bridges were developed in an effort to identify
the key components that allow characterization of torsional rotation displacements and the
lateral displacements as well as the LFB stress profile. A parametric analysis was performed
to single out the most sensitive parameters and to establish a possible mitigation strategy for
both the stresses and displacements. The study identified that increasing the polar moment of
inertia of the girders by slightly increasing the thickness of either the flanges or the web
produces more beneficial effects than the traditional idea of increasing the number of
crossframes or diaphragms along the span. The crossframe layout was also found to be
crucial on the rotational response of the bridge and the X-type crossframes proved to be more
efficient in controlling transverse rotations. On the other hand, it was determined that the
worst case scenario produced a maximum LFB locked-in stress of 18% of the yield stress.
Lateral Flange Bending in Heavily Skewed Steel Bridges
by
Francisco Javier Morera
A dissertation submitted to the Graduate Faculty of
North Carolina State University
in partial fulfillment of the
requirements for the Degree of
Doctor of Philosophy
Civil Engineering
Raleigh, North Carolina
2010
APPROVED BY:
Dr. James Nau
Chair of Advisory Committee
Dr. Emmett A. Sumner
Advisory Committee
Dr. Abhinav Gupta
Advisory Committee
Dr. Rudolf Seracino
Advisory Committee
ii
DEDICATION
To Marisol, Daniela, Alejandra and Andrea.
My wonderful family.
iii
BIOGRAPHY
Francisco Morera received his Bachelor of Science degree in Civil Engineering in 1991 from
Universidad Católica Andrés Bello, in Caracas, Venezuela. Then, in 1995 he moved to
Austin, Texas, where he pursued his Master of Sciences in Civil Engineering at The
University of Texas. In 1996 he completed his research on Statistical Analysis of Spar
Platform Response to Irregular Waves under the advisory of Dr. Jose Roesset and received
his Master in Sciences degree. Ten years later, he moved to Raleigh, North Carolina to
pursue his Doctoral degree, under the guidance of Dr. Emmett Sumner at North Carolina
State University.
iv
ACKNOWLEDGMENTS
To begin with I would like to thank both “Universidad Católica Andrés Bello” (UCAB) and
North Carolina State University (NCSU) whose confidence in me made it possible to achieve
this huge accomplishment in my life.
The author acknowledges the North Carolina Department of Transportation (NCDOT) for
providing the funding, information, assistance, and support to successfully bring about this
ambitious project. In particular, special thanks to Mr. Brian Hanks, of the NCDOT Structures
Division, for his continuous willingness and readiness to solve the different problems we ran
into throughout the investigation.
If there is one person that is truly worthy of my most sincere appreciation, that person is
undoubtedly Dr. Emmett Sumner. His commitment and dedication were paramount to the
success of this ambitious challenge, and I am sure that life will give me the pleasant
opportunity to pay him back all the invaluable guidance and effort in some way. On the
academic side, Dr. Rudolf Seracino was perhaps a unique role model, and having him as my
teacher of three different courses was not a coincidence. Dr James Nau, demonstrated to be a
good teaching mentor and friend. Dr. Sami Rizkalla whose academic and personal support
was priceless for the last four years. Although not directly related to my research, Dr. John
Stone always showed himself to be a wise person and his advice will always be truly
appreciated.
Upon arrival, my office was assigned at the Constructed Facilities Laboratory (CFL). It was
there that I met a group of wonderful people, like my officemate Chemin, whose patience
was out of the ordinary. Amy, Diana and Denise were always so forthcoming whenever I
needed them, that I do not have enough words to express my gratitude. Fabricio, Diego,
Lenny, Mina and many more will be forever remembered for their unconditional support.
v
Although most of my research activities did not required the use of the CFL equipment, Bill,
Greg, Jerry and Jonathan proved to be worthy of my admiration for their genuine help of
those times that I required them.
Without hesitation, I would like to express my most heartfelt thanks to my beautiful family.
To my wife, who walked alongside me on this journey and helped me when she did not have
the strength. To my daughters, the reason that gave me the power and motive that justified
this project.
Finally, I thank God that rules our lives in ways we sometimes struggle to understand.
vi
TABLE OF CONTENTS
LIST OF FIGURES ........................................................................................................................... xii
LIST OF TABLES ............................................................................................................................ xvi
CHAPTER 1. INTRODUCTION ................................................................................................. 1
CHAPTER 2. OBJECTIVES AND SCOPE ................................................................................. 3
2.1 General .................................................................................................................................................. 3
2.2 Literature Review .................................................................................................................................. 3
2.2.1 Construction Issues ............................................................................................................................. 4
2.2.2 Parametric Studies .............................................................................................................................. 6
2.2.2.1 Stay-in-Place (SIP) Metal Forms ................................................................................................. 6
2.2.2.2 Skew Angle ................................................................................................................................. 9
2.2.2.3 Cross-Frames / Diaphragms ..................................................................................................... 11
2.2.2.4 Lateral and Torsional Strength / Stiffness ................................................................................ 13
2.2.3 Steel Bridge Modeling ....................................................................................................................... 15
2.2.4 NCSU / NCDOT Related Studies ......................................................................................................... 25
2.2.5 Need for Research ............................................................................................................................. 27
2.3 Field monitoring of steel girders during placement of the bridge deck. ............................................... 28
2.4 Analytical investigation and quantification of lateral flange bending. ................................................. 28
2.5 Development of mitigation strategies .................................................................................................. 29
CHAPTER 3. FIELD MEASUREMENTS ................................................................................ 30
3.1 General ................................................................................................................................................ 30
3.2 Bridge Selection ................................................................................................................................... 30
vii
3.3 Bridges Studied .................................................................................................................................... 31
3.3.1 General Information. ......................................................................................................................... 31
3.3.2 Bridges Monitored ............................................................................................................................. 31
3.3.3 Bridge on SR 1003 (Chicken Road) over US 74 between SR 1155 & SR 1161 in Robeson County.
Project # R-513BB ............................................................................................................................................ 32
3.3.4 Bridge No 338 over Roaring Fork Creek on SR 1320 (Roaring Fork Road) in Ashe County. Project #
B-4013 33
3.4 Field Measurements ............................................................................................................................ 34
3.4.1 Overview ........................................................................................................................................... 34
3.4.2 Girder Cross Section Rotations. ......................................................................................................... 35
3.4.3 Temperature ...................................................................................................................................... 36
3.4.4 Sign Convention ................................................................................................................................. 36
3.4.5 Sources of Error ................................................................................................................................. 37
3.4.6 Limitations ......................................................................................................................................... 37
3.5 Summary of Acquired Field Data .......................................................................................................... 37
CHAPTER 4. FINITE ELEMENT MODELING ...................................................................... 39
4.1 Introduction ......................................................................................................................................... 39
4.2 General ................................................................................................................................................ 39
4.3 Bridge Components ............................................................................................................................. 39
4.4 Crossframes ......................................................................................................................................... 40
4.4.1 End Bent Crossframes and Diaphragms ............................................................................................ 40
4.4.2 Intermediate Crossframes ................................................................................................................. 41
4.4.3 Elastomeric Pads ............................................................................................................................... 42
4.5 Modeling Procedure ............................................................................................................................ 44
4.5.1 Initial Model (Model 1) ...................................................................................................................... 44
4.5.2 Next Model (Model 2) ....................................................................................................................... 45
4.5.3 Model 3. An improved discretization ................................................................................................ 49
viii
4.5.4 Model 4 Final Model ......................................................................................................................... 51
4.5.5 Validation of Results. ......................................................................................................................... 52
4.6 TIPS FOR MODELING ............................................................................................................................ 54
4.6.1 General .............................................................................................................................................. 54
4.6.2 Modeling Components ...................................................................................................................... 54
4.6.2.1 Girders and sole plates ............................................................................................................ 54
4.6.2.2 Connectors and stiffeners ........................................................................................................ 56
4.6.2.3 Diaphragms .............................................................................................................................. 56
4.6.2.4 Stay In Place Forms (SIP’s), K-type and X-type intermediate crossframes. ............................. 56
4.6.2.5 Bearing Supports. ..................................................................................................................... 57
4.6.2.6 End Bent Crossframes / Diaphragms ....................................................................................... 58
CHAPTER 5. A SIMPLIFIED MODEL PROCEDURE .......................................................... 59
5.1 Introduction ......................................................................................................................................... 59
5.2 Cross Section Rotations ....................................................................................................................... 60
5.3 Rigid Body Torsional Rotations ............................................................................................................ 61
5.4 The Rotations Profile ........................................................................................................................... 62
5.4.1 Inflection point Location (X0) ............................................................................................................. 64
5.4.2 The initial End rotations (i) .............................................................................................................. 65
5.4.3 The Final End rotations (f)................................................................................................................ 66
5.4.4 Slopes- Overview ............................................................................................................................... 67
5.4.4.1 Initial Segment Slope (mi) ........................................................................................................ 67
5.4.4.2 Middle Segment Slope (m0) ..................................................................................................... 68
5.4.4.3 Final Segment Slope (mf) ......................................................................................................... 69
5.5 The proposed simplified model ............................................................................................................ 70
5.5.1 Minimum and Maximum Locations (Xmin, Xmax) ................................................................................. 72
5.5.2 Minimum and Maximum Values (min, max) ..................................................................................... 74
5.5.3 Example. ............................................................................................................................................ 77
ix
5.6 Procedure to determine the Lateral Displacements (LD) on Steel skewed bridges due to lateral flange
bending. ........................................................................................................................................................ 78
5.6.1 Example. ............................................................................................................................................ 79
CHAPTER 6. PARAMETRIC ANALYSIS ............................................................................... 81
6.1 Overview ............................................................................................................................................. 81
6.2 Numerical Parameters. ........................................................................................................................ 81
6.2.1 General .............................................................................................................................................. 81
6.2.2 Exterior to Interior Moment of Inertia Ratio (Strong Axis) ............................................................... 83
6.2.3 Exterior to Interior Girder Load Ratio ................................................................................................ 86
6.2.4 Number of Girders ............................................................................................................................. 89
6.2.5 Number of Transverse Stiffeners ...................................................................................................... 92
6.2.6 Number of Crossframes..................................................................................................................... 95
6.2.7 Crossframe Stiffness .......................................................................................................................... 98
6.2.8 Stay in Place Forms Stiffness ........................................................................................................... 101
6.2.9 Girder Spacing to Span Ratio ........................................................................................................... 104
6.2.10 Analysis of Results ...................................................................................................................... 107
6.2.10.1 Favorable Parameters (Ratio > 5%) ........................................................................................ 107
6.2.10.2 Neutral Parameters (-5% ≤ Ratio ≤ 5%) ................................................................................. 108
6.2.10.3 Unfavorable Parameters (Ratio < -5%) .................................................................................. 109
6.2.10.4 Summary of Numerical Cases ................................................................................................ 110
6.3 Non-numerical Parameters ................................................................................................................ 111
6.3.1 Crossframe Layout. .......................................................................................................................... 111
6.3.1.1 Overview ................................................................................................................................ 111
6.3.1.2 Comparison of Results ........................................................................................................... 111
6.3.2 Crossframe Type (X-Type vs. K-Type) .............................................................................................. 115
6.3.2.1 General................................................................................................................................... 115
6.3.2.2 Preliminary Analysis ............................................................................................................... 115
6.3.2.3 Comparison of Results ........................................................................................................... 116
6.3.3 Dead Load Fit ................................................................................................................................... 118
6.3.3.1 Overview ................................................................................................................................ 118
x
6.3.3.2 General Procedure. ................................................................................................................ 118
6.3.3.3 Analysis of Results .................................................................................................................. 120
6.3.4 Pouring Sequence ............................................................................................................................ 124
6.3.4.1 Overview ................................................................................................................................ 124
6.3.4.2 Analysis of Results .................................................................................................................. 124
CHAPTER 7. LATERAL FLANGE BENDING STRESSES ................................................ 129
7.1 General .............................................................................................................................................. 129
7.2 Sources of Stress Concentration ........................................................................................................ 129
7.2.1 Stress concentrations at the End Bents. .......................................................................................... 130
7.2.2 Stress concentrations at the Intermediate Crossframes or Diaphragms ........................................ 131
7.2.3 Other possible sources .................................................................................................................... 131
7.3 The LFB stress profile ......................................................................................................................... 132
7.4 LFB stress profile characteristics ........................................................................................................ 138
7.4.1 Key Regions ..................................................................................................................................... 138
7.4.2 “Locked-in” Stresses due to LFB ...................................................................................................... 140
7.5 LFB stress profile analysis .................................................................................................................. 142
7.5.1 LFB vs. Torsional displacements ...................................................................................................... 142
7.5.2 LFB stresses vs. Torsional displacements. ....................................................................................... 144
7.5.3 LFB Stresses vs. Skew Angle ............................................................................................................ 145
CHAPTER 8. SUMMARY, OBSERVATIONS AND CONCLUSIONS .............................. 148
8.1 General .............................................................................................................................................. 148
8.2 Summary ........................................................................................................................................... 148
8.3 Outstanding observations .................................................................................................................. 149
8.4 Conclusions ........................................................................................................................................ 150
xi
CHAPTER 9. RECOMMENDATIONS AND FUTURE WORK ........................................ 154
APPENDICES ................................................................................................................................ 164
APPENDIX A-1 ............................................................................................................................. 165
APPENDIX A-2 ............................................................................................................................. 168
APPENDIX B ................................................................................................................................. 170
APPENDIX C .................................................................................................................................. 178
APPENDIX D ................................................................................................................................. 185
APPENDIX E.................................................................................................................................. 307
APPENDIX F .................................................................................................................................. 317
APPENDIX G ................................................................................................................................. 366
APPENDIX H ................................................................................................................................. 381
APPENDIX I................................................................................................................................... 396
xii
LIST OF FIGURES
FIGURE 3-1. CHICKEN ROAD BRIDGE .................................................................................................................... 33
FIGURE 3-2. ROARING FORK ROAD, IN ASHE COUNTY ......................................................................................... 34
FIGURE 3-3. PROCEDURE TO MEASURE ROTATIONS ON THE BOTTOM FLANGE (LEFT) AND WEB (RIGHT) ........ 35
FIGURE 3-4. PROCEDURE TO MEASURE ROTATIONS ON TOP FLANGES .............................................................. 36
FIGURE 3-5. LAYOUT OF INSTRUMENTATION ON ROARING FORK BRIDGE ... ERROR! BOOKMARK NOT DEFINED.
FIGURE 3-6. STRAIN TRANSDUCERS ON ONE OF THE END BENT DIAPHRAGMS ............ ERROR! BOOKMARK NOT
DEFINED.
FIGURE 3-7. DIRECTIONS OF POSITIVE ROTATIONS ............................................................................................. 36
FIGURE 3-8. IMPERFECTIONS OF THE STRAIGHTNESS .......................................................................................... 37
FIGURE 4-1. BOTH TYPES OF END BENT CROSSFRAMES CONSIDERED ................................................................. 40
FIGURE 4-2. COUPLING OF NODES AT BOLT LOCATIONS TO SIMULATE REAL INTERACTION .............................. 41
FIGURE 4-3. THREE TYPES OF INTERMEDIATE DIAPHRAGMS OR CROSSFRAMES ................................................ 42
FIGURE 4-4. CONSTRAINTS AT THE SUPPORTS ..................................................................................................... 43
FIGURE 4-5. GIRDERS END REGIONS ON MODEL 1 .............................................................................................. 44
FIGURE 4-6. SIP FORCE DISTRIBUTION ALONG THE SPAN .................................................................................... 45
FIGURE 4-7. SECOND MODEL DETAIL, INCORPORATING SIP'S ON THE END REGIONS ......................................... 46
FIGURE 4-8. FORCE DISTRIBUTION ALONG THE SIP'S IN MODEL 2 ...................................................................... 47
FIGURE 4-9. FORCE DISTRIBUTION BETWEEN SIP'S AND CROSSFRAMES ............................................................. 48
FIGURE 4-10. ROTATIONS COMPARISON BETWEEN MODELS 1 AND 2 AT TOP FLANGE ..................................... 49
FIGURE 4-11. MODEL 3 INCLUDING DIAPHRAGMS DISCRETIZED WITH SHELL ELEMENTS. ................................. 50
FIGURE 4-12. RELATIONSHIP BETWEEN SKEW ANGLE AND MAXIMUM DEFLECTIONS ....................................... 51
FIGURE 4-13. DETAIL OF THE END BENT CONNECTION IN THE FINAL MODEL (MODEL 4) .................................. 52
FIGURE 4-14. DETAIL OF THE MESH ON ONE OF THE GIRDERS OF ROARING FORK BRIDGE ................................ 55
FIGURE 4-15. END BENT DETAIL OF CHICKEN ROAD BRIDGE ............................................................................... 58
FIGURE 5-1. ROTATIONS ON THE GIRDER CROSS SECTION .................................................................................. 60
FIGURE 5-2. ROTATIONS AT 5 DIFFERENT LOCATIONS FOR ROARING FORK BRIDGE .......................................... 61
FIGURE 5-3. ROTATIONS PROFILE OF GIRDER 3 ON ROARING FORK BRIDGE ...................................................... 62
FIGURE 5-4. ROTATIONS PROFILE OF GIRDER 2 ON CHICKEN ROAD BRIDGE ....................................................... 63
FIGURE 5-5. COMPARISON BETWEEN NORMALIZED ROTATIONS IN BOTH BRIDGES .......................................... 64
FIGURE 5-6. VARIATION OF THE INFLECTION POINT LOCATION VS. SKEW ANGLE FOR BOTH BRIDGES .............. 65
FIGURE 5-7. INITIAL ROTATIONS OF CHICKEN ROAD BRIDGE (LEFT) AND ROARING FORK BRIDGE (RIGHT) ....... 66
xiii
FIGURE 5-8. FINAL ROTATIONS OF CHICKEN ROAD BRIDGE (LEFT) AND ROARING FORK BRIDGE (RIGHT).......... 66
FIGURE 5-9. INITIAL SEGMENT SLOPE VARIATION FOR BOTH BRIDGES ............................................................... 68
FIGURE 5-10. VARIATION OF THE MIDDLE SEGMENT SLOPE ............................................................................... 69
FIGURE 5-11. FINAL SEGMENT SLOPE VARIATION ............................................................................................... 69
FIGURE 5-12. PROPOSED SIMPLIFIED MODEL FOR MEAN VALUES ...................................................................... 70
FIGURE 5-13. PROPOSED REGION OF RESULTS FOR THE ROTATION PROFILE ..................................................... 71
FIGURE 5-14. DISTRIBUTION OF LOCATIONS OF MINIMUM ROTATIONS ............................................................ 73
FIGURE 5-15. LOCATIONS OF MAXIMUM ROTATIONS WITH RESPECT TO THE FINAL END OF THE TWO BRIDGES
........................................................................................................................................................ 73
FIGURE 5-16. LOW AND UPPER BOUND POINTS FOR THE MINIMUM VALUES .................................................... 74
FIGURE 5-17. LOWER AND UPPER BOUND ROTATIONS FOR THE MAXIMUM VALUES ........................................ 75
FIGURE 5-18. EXAMPLE OF THE LOWER AND UPPER BOUNDS ON ONE OF THE BRIDGES ................................... 76
FIGURE 5-19. GIRDER X SECTION .......................................................................................................................... 78
FIGURE 6-1. TYPICAL CROSS SECTION ON THE DEFLECTED SHAPE AT A GIVEN SECTION ALONG THE SPAN ....... 83
FIGURE 6-2. MINIMUM ROTATIONS FOR THE “EXTERIOR TO INTERIOR MOMENT OF INERTIA” CASE ............... 85
FIGURE 6-3. MAXIMUM ROTATIONS FOR THE “EXTERIOR TO INTERIOR MOMENT OF INERTIA” CASE .............. 85
FIGURE 6-4. MINIMUM ROTATIONS DISTRIBUTION FOR THE “EXTERIOR TO INTERIOR LOAD RATIO” CASE ...... 87
FIGURE 6-5. MAXIMUM ROTATIONS DISTRIBUTION FOR THE “EXTERIOR TO INTERIOR LOAD RATIO” CASE ..... 88
FIGURE 6-6. MINIMUM ROTATIONS DISTRIBUTION FOR THE “NUMBER OF GIRDERS” CASE .............................. 90
FIGURE 6-7. MAXIMUM ROTATIONS DISTRIBUTION FOR THE “NUMBER OF GIRDERS” CASE ............................. 91
FIGURE 6-8. ROARING FORK BRIDGE WITH N+5 GIRDERS (10 GIRDERS) ............................................................. 91
FIGURE 6-9. MINIMUM ROTATIONS DISTRIBUTION FOR THE “NUMBER OF STIFFENERS” CASE ......................... 93
FIGURE 6-10. MAXIMUM ROTATIONS DISTRIBUTION FOR THE “NUMBER OF STIFFENERS” CASE ...................... 94
FIGURE 6-11. DETAIL OF THE STIFFENERS DISTRIBUTION FOR THE 2.33X CASE ON CHICKEN ROAD BRIDGE ...... 94
FIGURE 6-12. ROTATIONS DISTRIBUTION FOR THE “NUMBER OF CROSSFRAMES” CASE .................................... 96
FIGURE 6-13. MAXIMUM ROTATIONS DISTRIBUTION FOR THE “NUMBER OF CROSSFRAMES” CASE ................. 97
FIGURE 6-14. ROARING FORK BRIDGE AT 75 DEG SKEW WITH TWICE THE ORIGINAL NUMBER OF
CROSSFRAMES ................................................................................................................................ 97
FIGURE 6-15. MINIMUM ROTATIONS DISTRIBUTION FOR THE “CROSSFRAMES STIFFNESS” CASE ..................... 99
FIGURE 6-16. MAXIMUM ROTATIONS DISTRIBUTION FOR THE “CROSSFRAMES STIFFNESS” CASE .................. 100
FIGURE 6-17. MINIMUM ROTATIONS DISTRIBUTION FOR THE “STAY IN PLACE FORMS STIFFNESS” CASE ....... 102
FIGURE 6-18. MAXIMUM ROTATIONS DISTRIBUTION FOR THE “STAY IN PLACE FORMS STIFFNESS” CASE ...... 103
FIGURE 6-19. MINIMUM ROTATIONS DISTRIBUTION FOR THE “SPACE TO SPAN RATIO” CASE ........................ 105
xiv
FIGURE 6-20. MAXIMUM ROTATIONS DISTRIBUTION FOR THE “SPACE TO SPAN RATIO” CASE........................ 106
FIGURE 6-21. ROARING FORK BRIDGE WITH A 75 DEG SKEW AND A SPACE / SPAN RATIO HALF OF THE
ORIGINAL ....................................................................................................................................... 106
FIGURE 6-22. RESULTS FROM THE STUDY ON NUMERICAL PARAMETERS ......................................................... 110
FIGURE 6-23. LAYOUTS CONSIDERED: STAGGERED (LEFT), PARALLEL (CENTER) AND PERPENDICULAR (RIGHT)
...................................................................................................................................................... 111
FIGURE 6-24. ROTATIONS ON CHICKEN RD. (LEFT) AND ROARING FK. RD (RIGHT) BRIDGES ............................ 112
FIGURE 6-25. AVERAGE MAXIMUM STRESSES ON CHICKEN RD. (LEFT) AND ROARING FK. RD (RIGHT) BRIDGES
...................................................................................................................................................... 112
FIGURE 6-26. TOTAL CROSSFRAME FORCES FOR THE THREE SKEW ANGLES STUDIED. (A) CR 25 (B) CR 43
(C) CR 75 (D) RF 23 (E) RF 45 (F) RF 75 .......................................................................................... 114
FIGURE 6-27. PLAN VIEW OF THE THREE CROSSFRAME LAYOUTS OVERLAPPED FOR 75 DEGREE SKEW ON
CHICKEN RD. BRIDGE..................................................................................................................... 114
FIGURE 6-28. CROSSFRAME AND UNIT LOAD CONFIGURATIONS ...................................................................... 115
FIGURE 6-29. DISTRIBUTION OF ST. VENANT’S ROTATIONS VERSUS SKEW ANGLE ON CHICKEN ROAD BRIDGE
...................................................................................................................................................... 117
FIGURE 6-30. INITIAL (STATE A) AND FINAL (STATE B) CONDITIONS OF A CROSS SECTION ON A STRAIGHT
SKEWED BRIDGE. ........................................................................................................................... 119
FIGURE 6-31. INITIAL (STATE C) AND FINAL (STATE D) CONDITIONS OF A CROSS SECTION ON A CAMBERED
SKEWED BRIDGE ............................................................................................................................ 120
FIGURE 6-32. DISTRIBUTION OF THE DIFFERENCE IN STRESSES ON AN EXTERIOR GIRDER BETWEEN THE
CAMBERED AND THE STRAIGHT MODELS AT THE TOP FLANGE ON A 23 DEG. SKEW ANGLE
BRIDGE .......................................................................................................................................... 121
FIGURE 6-33. DISTRIBUTION OF THE DIFFERENCE IN STRESSES ON AN EXTERIOR GIRDER BETWEEN THE
CAMBERED AND THE STRAIGHT MODELS AT THE BOTTOM FLANGE ON A 23 DEG. SKEW ANGLE
BRIDGE. ......................................................................................................................................... 121
FIGURE 6-34. DISTRIBUTION OF NORMALIZED ROTATIONS AND THEIR DIFFERENCE FOR AN EXTERIOR GIRDER
ON A 23 DEGREE SKEW ANGLE ..................................................................................................... 122
FIGURE 6-35. DISTRIBUTION OF NORMALIZED ROTATIONS AND THEIR DIFFERENCE FOR AN INTERIOR GIRDER
ON A 23 DEGREE SKEW ANGLE. .................................................................................................... 123
FIGURE 6-36. DISTRIBUTION OF THE DIFFERENCE IN LFB STRESSES ON AN EXTERIOR GIRDER BETWEEN THE
POURING SEQUENCE ADOPTED AND THE ORIGINAL MODEL AT THE TOP FLANGE ON A 45 DEG.
SKEW ANGLE BRIDGE. ................................................................................................................... 125
xv
FIGURE 6-37. DISTRIBUTION OF THE DIFFERENCE IN LFB STRESSES ON AN EXTERIOR GIRDER BETWEEN THE
POURING SEQUENCE ADOPTED AND THE ORIGINAL MODEL AT THE BOTTOM FLANGE ON A 45
DEG. SKEW ANGLE BRIDGE. .......................................................................................................... 125
FIGURE 6-38. DISTRIBUTION OF NORMALIZED ROTATIONS AND THEIR DIFFERENCE FOR AN EXTERIOR GIRDER
ON A 45 DEGREE SKEW ANGLE ..................................................................................................... 127
FIGURE 6-39. DISTRIBUTION OF NORMALIZED ROTATIONS AND THEIR DIFFERENCE FOR AN INTERIOR GIRDER
ON A 45 DEGREE SKEW ANGLE. .................................................................................................... 128
FIGURE 7-1. LONGITUDINAL STRESS CONTOURS AT THE END BENTS. ............................................................... 130
FIGURE 7-2. STRESS CONCENTRATIONS ALONG THE SPAN ON TOP AND BOTTOM FLANGES ........................... 131
FIGURE 7-3. COMBINED LONGITUDINAL STRESSES ON A GIRDER SECTION ...................................................... 133
FIGURE 7-4. TOTAL STRESS DISTRIBUTION ON TOP FLANGE OF AN EXTERIOR GIRDER ..................................... 134
FIGURE 7-5. TOTAL STRESS DISTRIBUTION ON BOTTOM FLANGE OF AN EXTERIOR GIRDER ............................. 134
FIGURE 7-6. TOTAL STRESS DISTRIBUTION ON TOP FLANGE OF AN INTERIOR GIRDER .................................... 135
FIGURE 7-7. TOTAL STRESS DISTRIBUTION ON BOTTOM FLANGE OF AN INTERIOR GIRDER ............................. 135
FIGURE 7-8. NORMALIZED LFB STRESS PROFILE FOR ON THE TOP FLANGE OF AN EXTERIOR GIRDER .............. 136
FIGURE 7-9. NORMALIZED LFB STRESS PROFILE FOR ON THE BOTTOM FLANGE OF AN EXTERIOR GIRDER ...... 137
FIGURE 7-10. NORMALIZED LFB STRESS PROFILE FOR ON THE TOP FLANGE OF AN INTERIOR GIRDER ............ 137
FIGURE 7-11. NORMALIZED LFB STRESS PROFILE FOR ON THE BOTTOM FLANGE OF AN INTERIOR GIRDER .... 138
FIGURE 7-12. KEY REGIONS ON A TYPICAL LFB STRESS PROFILE ........................................................................ 139
FIGURE 7-13. BOTTOM FLANGE (LEFT) AND TOP FLANGE (RIGHT) DISPLACEMENTS ........................................ 142
FIGURE 7-14. LFB STRESSES VS. ROTATIONS ON THE BOTTOM FLANGE ............................................................ 145
FIGURE 7-15. MAXIMUM STRESS VALUES FOR CHICKEN ROAD BRIDGE VERSUS SKEW ANGLE. ....................... 146
FIGURE 7-16. MAXIMUM STRESS VALUES FOR ROARING FORK ROAD BRIDGE VERSUS SKEW ANGLE. ............. 146
xvi
LIST OF TABLES
TABLE 3-1. LIST OF POTENTIAL BRIDGES TO BE INCLUDED IN THE STUDY (SOURCE: NCDOT) ............................. 31
TABLE 3-2 SUMMARY OF BRIDGES ....................................................................................................................... 32
TABLE 3-3. SUMMARY OF GIRDER ROTATIONS, IN DEGREES, RECORDED FOR BOTH BRIDGES ........................... 38
TABLE 4-1 GEOMETRICAL PROPERTIES OF THE GIRDERS ..................................................................................... 54
TABLE 5-1. SUMMARY OF MINIMUM AND MAXIMUM LOCATIONS .................................................................... 74
TABLE 5-2. VALUES AND LOCATION OF MINIMUM AND MAXIMUM ROTATIONS ............................................... 76
TABLE 5-3. VALUES FOR 60 DEG SKEW ................................................................................................................. 77
TABLE 6-1. ROTATION VALUES FOR THE “EXTERIOR TO INTERIOR MOMENT OF INERTIA” CASE ........................ 84
TABLE 6-2. ROTATION VALUES FOR THE “EXTERIOR TO INTERIOR GIRDER LOAD RATIO” CASE .......................... 86
TABLE 6-3. ROTATION VALUES FOR THE “NUMBER OF GIRDERS” CASE .............................................................. 89
TABLE 6-4. ROTATION VALUES FOR THE “NUMBER OF STIFFENERS” CASE ......................................................... 92
TABLE 6-5. ROTATION VALUES FOR THE “NUMBER OF CROSSFRAMES” CASE .................................................... 95
TABLE 6-6. ROTATION VALUES FOR THE “CROSSFRAME STIFFNESS” CASE .......................................................... 98
TABLE 6-7. ROTATION VALUES FOR THE “STAY IN PLACE FORMS STIFFNESS” CASE .......................................... 101
TABLE 6-8 ROTATION VALUES FOR THE “GIRDER SPACE TO SPAN RATIO” CASE ............................................... 104
TABLE 7-1. BOUNDS FOR THE STABLE REGION. ................................................................................................. 140
TABLE 7-2. SUMMARY OF STRESSES ON THE BOTTOM FLANGE ........................................................................ 141
TABLE 7-3. SUMMARY OF STRESSES ON THE TOP FLANGE ................................................................................ 141
TABLE 7-4. SUMMARY OF LATERAL DISPLACEMENTS ON THE BOTTOM FLANGE .............................................. 143
TABLE 7-5. SUMMARY OF LATERAL DISPLACEMENTS ON THE TOP FLANGE ...................................................... 143
TABLE 7-6. SUMMARY OF LFB DISPLACEMENTS ................................................................................................ 144
1
CHAPTER 1. INTRODUCTION
Nowadays it is becoming more common the need to use heavily skewed bridges to more
easily deal with site constraints and to accommodate the more demanding geometries. In
consequence it becomes mandatory to understand the complex behavior of these types of
structures with a higher degree of accuracy.
The problem related to lateral flange bending of steel plate skewed girders during the non
composite phase of construction can be simply stated as a consequence of the significant
support skew, typical staggered crossframes along the span in between adjacent girders,
differential deflections commonly present on skewed bridges, out of plumb condition
associated with girder camber and imperfections, and the force transfer mechanism due to the
overhang falsework. However technically speaking, this phenomenon is the result of out of
plane rotations due to torsional moments acting on the girders because of unsymmetrical
distribution of forces and constraints throughout the whole structure.
Current AASHTO design specifications address this issue by considering the evident
difficulties arising from this situation that lead to costly delays and the potential need for
further analysis to account for the additional stresses on girders, crossframes and bearings as
well as potential sources of undesirable problems such as fatigue and durability issues.
Nonetheless, the available information related to this condition is scarce, hence an extensive
investigation was carried out with the primary objective of understanding the out of plane
torsional rotation phenomenon by means of a comprehensive parametric analysis, including
quantifying the effects of each parameter, evaluating and predicting the response, and
providing some insight of possible remedies to mitigate the eventual undesirable outcomes.
In an effort to properly evaluate the out of plane rotation condition, two steel plate girder
bridges were selected, in accordance with the NCDOT, and monitored during placement of
the concrete deck to observe the rotations of the girders at different locations along the span.
2
From previous investigations, carried by Whisenhunt (2004) and Fisher (2005), the finite
element models used were modified to account for the effects of stay in place forms along the
entire span, gusset plates, and elastomeric pads on the overall behavior of the structure,
utilizing ANSYS V.11 as the software platform. Once the model was sufficiently improved,
a computational program was developed to facilitate the generation of the necessary input
data to carry out the parametric analysis, where more than 180 cases were studied to not only
determine the sensitivity of the system to each parameter, but to develop a simplified model
to predict the out of plane rotation profile of the structure as well as the overall magnitude of
the possible locked-in stresses due to lateral flange bending during the construction phase.
With the information gathered from the analysis it was possible to generate a proposed
mitigation scheme, on which it was demonstrated that some variations in certain parameters
either enhanced the rotational response of the structure (favorable changes), did not produce
a major effect whatsoever (neutral changes) or decreased the ability of the girders to
withstand the external conditions ( unfavorable changes).
With this information, Lateral Flange Bending (LFB) stresses were thoroughly studied to
gain a detailed understanding of the factors influencing the response of the girder. From the
total bending stresses acting on the flanges, the LFB component was singled out and
compared to the corresponding yield stress. Additionally the LFB displacement and stress
profile were compared to determine the overall influence of each component of displacement
(lateral or rotational) on the bridge behavior. It was found that the LFB lateral displacement
component was negligible and the torsional rotation component governed the phenomena.
3
CHAPTER 2. OBJECTIVES AND SCOPE
2.1 General
The primary objectives of the proposed research are to quantify the lateral flange bending of
steel plate girders in heavily skewed bridges, develop a methodology for predicting the
magnitude of lateral translation of the girder flanges due to this effect, and establish
recommended strategies for mitigating the effect of heavy skew.
In order to achieve such objectives and as part of the research methodology, a series of tasks
were completed. These tasks are as follows:
2.2 Literature Review
An extensive literature review is conducted herein. It will be clear that information directly
related to quantifying lateral flange bending in steel plate skewed bridges is scarce.
Nevertheless, related research to the topic has been done. Parameters like skew angle, type of
bearing, stay-in-place (SIP) forms, cross-frames and/or diaphragms, overhang falsework,
torsional, and lateral stiffness of steel girders are among the most important variables to be
taken into account in the investigation. Additionally, influence of the non composite and
composite construction phases in the girder torsional behaviour as well as a finite element
modelling to understand the skewed system are also presented.
To facilitate the understanding of the topics presented, this review was divided into the
following sections: construction issues, parametric studies, steel bridge modelling,
NCSU/NCDOT related studies, and a final discussion about the need for research.
4
2.2.1 Construction Issues
Back in the early 70‟s the problem related to skewed bridges had already been pinpointed.
Hilton (1972) observed that during deck pouring, there are various issues that the designer
should account for such as non-uniform deck thickness along the span and the differential
temperatures existing between the top and bottom flanges on the girders, which may differ
from temperatures when forming elevations were established. Measurements were taken
from various bridges, using instruments such as thermocouples, high precision levels, and
special design rod and scale units. Gathered field data was compared to theoretical data
obtained using an analysis of semi-rigidly connected girders, which turned out to be in good
agreement with the field deflections. It was detected that the girder deflections would be
considerably greater if differential thermal conditions did not exist. However, the most
important finding was that resulting predictions tended to be larger than measured data in the
field on account of the bridge superstructure deflecting as a unit, rather than individual
girders.
The problem studied by Swett (1998) and Swett et al (2000), in response to WSDOT, was
how to control the inherent constructability issues that arise while either widening an existing
bridge or during a staged construction, particularly for straight bridges without significant
skew. It is desirable that the new structure ends up having the same elevation and cross slope
as the existing structure, after placing the concrete deck. This problem becomes more critical
when the new structure is not symmetric, since torsional moments will cause the bridge to
twist. To solve this, six different design and construction methodologies were presented, with
their corresponding pros and cons as well as applicable situations. Via Finite Element
Analysis (FEA) it was possible to compare actual deflections with those given by the model,
in order to evaluate the accuracy of the six methodologies. It turns out that there is no
universal solution, though appropriate choices of construction sequences can lead to
significant reductions in both unwanted deflections and locked-in stresses.
5
Another unique situation related to steel skewed bridges is the differential deflections. To
address this condition AASHTO/NSBA (2003) stated that girder deflections under dead load
for skewed bridges are not equal across the width of the bridge making it difficult to install
cross-frames at locations with significant differential deflection. Therefore, once cross-
frames are installed in these situations, they may restrain deflections causing girders to rotate
out of plumb and lateral stresses to be induced in the flanges. Additionally, if the girders are
required to be plumb under full dead load or steel dead load engineers should address the
expected rotations in advance under the applied dead load even though the anticipated
rotations are only a prediction and that actual rotations will likely be different, and therefore
girders will be somewhat out of plumb.
On the other hand, for cross-frames at skewed piers or abutments the major source of
problem is the rotation of the girders at those locations. In a square bridge, rotation of the
girders at the bearings is in the same plane of the girder web whereas when supports are
skewed, girder rotation due to non-composite loads will be normal to the piers or abutments.
This rotation displaces the top flange transversely from the bottom flange and causes the web
to be out of plumb. The type of bearing (elastomeric, pod, spherical, etc.) used plays an
important role because if bearings can tolerate the rotation and no other problems are present,
the situation may be acceptable. However, the designer should look at the size and capacity
of end cross-frame members for the degree of skew and the out-of-plumb bearing. This
bearing problem had been mentioned in the early 80‟s.
Burke (1983) focused his study mainly on describing different types of bearing systems that
can accommodate typical displacements developed by girder ends of skewed bridges, such as
rotations and lateral translations. Four different types of bearings were described in great
detail: Pot, spherical, disk, and elastomeric bearings. It was also noted that, particularly for
skewed and curved bridges, designers should account for rotations and translations at the
supports as a result of live loads. This particular phenomenon is often ignored and designers
6
only consider vertical deflections, so it is common to observe problems associated with the
bearings, such as fatigue cracks, in those bridges with considerable skewness.
Norton (2001) and Norton et al. (2003) used the information obtained from measurements on
an actual skewed steel bridge during deck pouring to compare the theoretical deflections and
rotations of the girders vs. the actual displacements. Parameters like screed orientation, deck
pouring sequence, dimension of the model (2D vs. 3D) were considered. It was noted that the
structure had the particular characteristic that the webs were out of plumb prior to concrete
pouring.
Of particular importance was that the 3D model was more accurate than the 2D. The deck
pouring sequence had no major effect on the forces developed at the crossframes if the
concrete is assumed to be plastic, though when pouring the concrete perpendicular to the
center line of the bridge leads to higher support reactions and displacements during the
intermediate stages of construction. It is worth mentioning that both rotations and lateral
displacements were considered linear along the girder web and while lateral displacements
did not match what was predicted, measured vertical displacements did.
2.2.2 Parametric Studies
2.2.2.1 Stay-in-Place (SIP) Metal Forms
Helwig (1994) conducted an investigation to determine the bracing capacity of SIP metal
forms, involving both experimental and analytical studies. The experimental studies,
previously carried out by Currah (1993) and Soderberg (1994), consisted of a series of tests
on isolated decks to determine their shear capacity, various deck to girder connections, and
buckling of twin girders with SIP metal forms. The dissertation covered the analytical
research done by using a FEA with the finite element program ANSYS to compute the
bracing effect given by the SIP metal forms to the girders. Parameters such as shear rigidity
of the deck, shape of girder cross section, in plane boundary conditions, number of transverse
7
stiffeners, type of loading, and load height were considered. It was determined that for
simply supported or continuous girders, considering the effects of moment gradient, load
height and cross section distortion either from web bend or shear buckling, the design
approach was reasonably accurate. From all these considerations it was possible to confirm
that lateral torsional buckling at the supports is only critical after completion of the bridge,
but by accounting the lateral stiffness given by the SIP forms it is possible to eliminate
crossframes, with the consequent benefits such as fewer weak points in terms of fatigue and a
structure easier to erect.
Few years later, Jetann et al. (2002) and Egilmez et al. (2007) developed a practical and
economical method to improve the strength and stiffness of the connection between SIP
metal forms and the girders. This was done by measuring the bracing behavior of metal deck
forms with both existing and new stiffer connections. The process included experimental and
computational studies, including parameters such as metal gauge of deck forms, support
angle connection details and panel aspect ratio. The outcome was that for systems with
eccentric connections details, stiffening angles spaced roughly twice the span of the
diaphragm would suffice both effectively and economically.
The diaphragm behavior the SIP forms was also studied. By conducting both experimental
(lab tests) and analytical (FEA) research Egilmez et al. (2003) were able to determine that
SIP forms add both shear and flexural stiffness. In this sense, it is worth mentioning that the
experiments were conducted on a full scale 50 ft. span twin girder with SIP fastened to the
top flanges and the results were compared to a finite element analysis to develop a more
accurate model of the bracing behavior. Results demonstrated that it is not good practice to
model SIP forms as a shear diaphragm since it tends to significantly underestimate bracing
behavior. On the other hand, it was demonstrated that incorporating additional “in deck
plane” bracing elements, such as angles connected in a truss shape configuration, the FEA
can account for the additional stiffness not present in the shear diaphragm model.
8
Egilmez and Helwig (2004) continued the work by Jetann et al. (2002) on shear tests and
Egilmez et al. (2003) on full scale lateral displacements tests on a twin girder system with
SIP forms for bracing. This time the research was focused on buckling tests as well as results
from the FEA. The experiments were carried out with the same configuration used on the
previous phases and including a gravity load simulator to apply transverse load to the system.
Lateral displacements were recorded and three different sets of 20 gauges deck forms were
placed on the beams.
In order to account for imperfections, the worst scenario was considered while setting up the
system. This included placing the support angles at their maximum eccentricity and
simulating the most critical shape imperfection for torsional bracing systems in beams that
occurs when the top flange experiences a displacement equal to the unbraced length divided
by 500, as shown by Wang and Helwig (2003). To account for this condition, a three phase
test was carried out including no offset, loads offset by half an inch in one direction, and load
offset to simulate the Lb/500d initial twist imperfection, where d is the depth of the cross
section. The results from the FEA, which included the effect of imperfections, were in good
agreement with the test results. Finally, test results revealed that a stiffened deck system
provides better control of the deformations when compared to the unstiffened systems.
Egilmez et al.(2006) continued the investigation in both experimental and computational
studies performed on permanent metal deck forms (PMDF) by Jetann et al. (2002) and
Egilmez et al. (2003, 2004 and 2005). This paper presented results from the computational
study on the stiffness requirements for PMDF used for stability bracing of steel bridge
girders. Research consisting of three testing phases was conducted. The first phase involved
testing to determine shear properties of metal deck forms. The second phase focused on
measuring the lateral stiffness of the PMDF panels when subjected to deformations similar to
the actual deflected top flange profile of buckled girders. The final phase was related to
buckling tests on twin girder systems with PMDF for bracing.
9
As far as the computational studies, a three dimensional finite element study was
implemented to perform parametric analysis on the behavior of steel I girders braced with
PMDF, using ANSYS as the software package. The PMDF was modeled as shear
diaphragms by means of truss panels, considering a distance of 16 ft between stiffening
angles. Parameters like girder span to depth ratio, girder cross section, and shear rigidity of
the deck system were also taken into account. An elastic eigenvalue buckling condition was
analyzed to determine the critical buckling load of the system. In order to account for the
effects of imperfections in the system geometry, a large displacement finite element analysis
was performed to determine that as the depth and length of the girders increase, so does the
stiffness requirements to control deformations, and therefore a limit on the unbraced length
for girders braced with PMDF should be established.
2.2.2.2 Skew Angle
Gupta and Kumar (1983) tested five small scale models with skew angles within 0 to 40
degrees. They found during their research, that there were 2 main issues to be considered:
skew angle and contribution of the slab to the girders. The study included both experimental
and analytical research. The analytical portion consisted of a FEA of the slab – girder
interaction. It was concluded that for a skew angle less than 30 degrees, skewness has little
effect and for angles higher than that, the moments, rotations, and deflections increase with
the increase in the skew angle, but the reactions in the loaded girder decrease. They also
pointed out that deflections and moments are greatly reduced by restraining the girder ends.
Bakht (1988), proposed an alternate parameter instead of the traditional skew angle. This
parameter was defined by means of three variables: the girder spacing S, the bridge span L,
and the angle of skew ( S tan / L). For values of this parameter less than 0.05, it is safe to
analyze the bridge as non skewed.
10
An investigation by Bishara and Elmir (1990) was conducted to develop a three dimensional
finite element algorithm to determine internal forces in end and intermediate crossframes on
composite steel bridges. Four steel bridges were analyzed, three of them skewed, and it was
found, among other things, that for skewed bridges most members of intermediate
crossframes develop the maximum compressive forces on those attached to the ends of
exterior girders close to the obtuse angles and maximum tensile forces occur on the chord
members at midspan. If the skew angle is increased, forces on the crossframes also increase.
A similar situation occurs if the sizes of the crossframes are increased as well, but for
crossframe members on the girder ends whose size was not changed, the internal forces were
not affected if intermediate crossframes were changed. The maximum differential deflections
occurred between the exterior girders and those adjacent to them close to the obtuse angle
and the torsional moments developed on the girders never exceeded 2% of the maximum
bending moment.
Berglund and Schultz (2006) focused their investigation on three things: the development of
a Finite Element Model (FEM) model to accurately predict the vertical differential
deflections between adjacent girders, a parametric study to determine the key components on
relative deflection on skewed bridges, and a technique to determine both the vertical
differential deflections and their inherent distortional stresses. The FEM was implemented
using SAP2000 Nonlinear as the software package. The three dimensional model included
shell elements for the deck and girder webs and frame elements to model girder flanges and
concrete railing. The composite behavior was modeled by using rigid frame elements as a
connection component. The parametric study included three primary parameters: span length,
angle of skew, and girder spacing. The secondary parameters were deck thickness, girder
spacing, adjacent span length, and diaphragm depth. As a result of the investigation a
formula to represent the variation of the differential deflection was determined. /S = (aL2 +
bL +c) / L , where L is the span length, S the girder spacing, the differential deflection, and
a, b and c are coefficients depending upon the angle of skew.
11
Other findings indicate that the higher the skew angle the higher the differential deflections,
the maximum diaphragm deflections occur on the obtuse corner of each loaded lane, longer
bridges do not undergo high differential deflections and the relationship between differential
deflections and girder spacing is linear.
2.2.2.3 Cross-Frames / Diaphragms
Shi (1997) addressed the fact that an adequate bracing system for lateral torsional buckling
must satisfy both stiffness and strength requirements, therefore special attention must be
given to the design of these components of a steel girder bridge. He mentioned that the
critical stage for buckling of steel girders takes place during deck pouring, therefore
providing intermediate crossframes or diaphragms not only solves this problem, but helps the
negative moment region to resist wind load on the girder bottom flange. Usually, crossframes
and diaphragms are built stiffer than needed (using the 2% method), leading to a
development of larger forces which induce fatigue problems at their locations. The research
included the evaluation of the buckling behavior of a simply supported twin girder system
with discrete torsional braces by using a FEA. Parameters like skew angle, load type, load
height, cross section shape, and brace orientation relative to skew angle were also considered.
Finally, Shi (1997) modified previous formulas developed for normal girders to determine
both the capacity and the stiffness of the crossframes.
According to Helwig and Wang (2003), AASHTO provisions are not clear enough when
referring to the design of bracing systems. This leads to possible greater sections in
crossframes and diaphragms than actually needed and subsequently to fatigue prone locations
along the girder. The main purpose of the investigation was to clarify the bracing
requirements for bridge girders so that properly sized braces can be employed, as well as to
provide details to minimize fatigue damage. To do this, a FEA was developed based upon
previous laboratory testing and then compared results with proposed equations for the design
requirements of crossframes and diaphragms. Helwig and Wang (2003) compared the results
12
for bridges with normal supports-stiffness and strength requirement, bridges with skewed
supports-parallel braces-stiffness and strength requirement, and bridges with skewed
supports-normal braces-stiffness and strength requirement. To finally enhance the buckling
capacity of the girders, slight modifications are needed on the strength requirements. For
girders with skewed supports and bracing perpendicular to the center line, the FEA was in
good agreement with the equations for non skewed supports. However, simple modifications
are required for bridges with skewed supports and bracing parallel to the skew angle.
Regarding AASHTO LRFD Bridge Design Specifications (2004), it is worth mentioning that
the requirement for diaphragms spaced at no more than 25 ft. is no longer valid. Instead it
was replaced by a requirement for rational analysis that could eventually lead to the
elimination of fatigue prone details. Additionally, flange lateral bending may be caused by
“wind, by torsion from eccentric concrete deck overhang loads acting on cantilever forming
brackets placed along exterior girders, and by the use of staggered cross-frames in
conjunction with skews exceeding 20º ”. In these cases, it is up to the design engineer to
consider the flange lateral bending, usually addressed by the use of refined analysis methods,
though it is not strictly required. Some of these effects have not been previously mentioned.
Herman et al. (2005) provided a thorough discussion of the lean-on bracing concepts and an
overview of one of the implementation bridges on which the bracing is being utilized
(TxDOT Study 0-1772).
The research study included examinations of intermediate bracing systems framed both
parallel to the skew and perpendicular to the longitudinal axis of the girders. By simply
modifying the bracing strength and stiffness expressions developed by Yura (2001) for
bridges with normal supports, it was possible to account for the impact of brace or support
skew angles as discussed by Helwig and Wang (2003). In addition to modifying the bracing
design expressions to account for the impact of support skew, details were also recommended
13
in TxDOT Study 0-1772 (2003) to both reduce the number of intermediate braces required
and to lessen the forces induced in these braces due to truck traffic.
The lean-on concept gives the engineer the flexibility of selecting positions for the cross-
frames within a given bracing line to minimize the cross-frame forces induced by truck
traffic in the completed bridge. To minimize the forces induced in the cross-frames by truck
traffic, the transverse position of the cross-frames should be selected such that they are as far
away from the support as possible, because for cross-frames positioned near support
locations the relative deflection across the cross-frame induces large cross-frame forces. By
positioning the cross-frames away from the supports at locations with smaller relative
vertical girder deflection the brace forces induced from live loading can be reduced.
The lean-on layout also produces a reduction in the total number of cross-frames required on
the bridge, and subsequently less fatigue prone points The implementation scheme was
conducted on three skewed bridges, all of which are two-span continuous systems with
severe support skews of 50 to 60 degrees. The outcome was that using a conventional layout
for the cross-frames, with cross-frames across the width of the bridge at every intermediate
cross-frame line, one of the bridges with nine girders would have required 128 intermediate
cross-frames, however 35 intermediate cross-frames would be required using the lean-on
system. It is imperative that every single girder would be braced. As long as intermediate
cross-frames are placed between each girder, a smooth transverse profile, analogous to that
seen with conventional cross-frame layouts, can be obtained.
2.2.2.4 Lateral and Torsional Strength / Stiffness
A comprehensive view of the beam bracing stability was conducted by Yura (1993). Beam
bracing systems such as lateral and torsional bracings were evaluated in great detail. It is
noteworthy the fact that both strength and stiffness of the brace system must be checked for
design purposes. Current published bracing requirements for beams do not account for out-
14
of-straightness, and should not be used in design. Similarly, design of those systems based on
the 2% rule could eventually lead to inadequate brace systems (usually over designed).
Using BASP (Akay, 1977; Choo, 1987), an elastic FE software that considers local and
lateral-torsional buckling including cross-section distortion, it was possible to solve different
loading and support cases for beams braced at different locations. For the case of lateral
bracing of beams the results indicated that because of cross section distortion and top flange
loading effects, lateral braces at the centroid are not recommended. Instead, lateral braces
must be placed near the top flange for many support conditions, and although loading
through the deck can provide a beneficial tipping effect that increases the buckling capacity,
it is not recommended to be considered in design. On the other hand, when a beam is
expected to be subjected to both positive and negative moment along its span, not only it is
incorrect to assume that the inflection point is the most suitable brace point but also that
bracing requirements for beams with double curvature are greater than those with single
curvature.
Additional analysis was conducted evaluating parameters like the number of bracing points
along the span of the beam. This analysis led to the conclusion that moment gradient, brace
location, load location, brace stiffness, and number of braces affect the buckling capacity of
laterally braced beams. The analysis ultimately made it possible to develop design
recommendations that account for all the previous conclusions. Torsional bracing of beams
was also considered, conducting the same tests used for laterally braced beams. It was shown
that torsional bracing is less sensitive than lateral bracing to conditions like top flange
loading, brace location, and number of braces, but more affected by cross-section distortion.
Additional studies by Yura (1999) covered four different types of bracing: relative, discrete,
continuous, and lean-on. Relative bracing is considered to control the relative movement of
points along the beam or to prevent relative displacement of the top and bottom flanges.
Discrete bracing controls the movement at a particular point (cross-frames/diaphragms).
15
Continuous bracing is attached to the beam along its length (SIP forms), and lean-on systems
are those on which the element relies on adjacent structural members for support. In these
particular systems structural members are linked to one another so the buckling of one of
them will require adjacent members to buckle with the same lateral displacement. In any
case, both stiffness and strength properties must be satisfied, considering that out-of-
straightness condition of the element plays an important role.
As far as beam bracing is concerned, only relative and discrete lateral bracing requirements
were considered. Both lateral and torsional bracing were discussed and particular
considerations were given to define what a brace point is, since in many cases the inflection
point of the buckling deformed shape is not located at those points. Hence, as long as the two
flanges move laterally the same amount, twist will not be present, and in such a case the
beam can be considered braced. Additionally, expressions included in LRFD for determining
strength and stiffness on systems with lateral bracing were presented along with design
examples.
For torsional bracing only cross-frames / diaphragms and metal decks or slabs are considered
as discrete or continuous torsional bracing systems respectively. However, it was found that
factors that had a significant effect on lateral bracing, such as number of bracings, top flange
loading, and brace location did not produce similar effects for torsional bracing. A torsional
brace is equally effective if it is attached to either the tension or compression flange.
Nevertheless, the effectiveness of a torsional brace is greatly affected by the cross section
distortion at the brace point, so web stiffeners are highly recommended.
2.2.3 Steel Bridge Modeling
During the early 80‟s, an extensive FE study was performed by Schilling (1982) in order to
develop lateral distribution factors suitable for use in fatigue calculations. The study
consisted of modeling 500 combinations of bridge configuration and load position with the
16
help of the general purpose finite element program ANSYS. Parameters such as number of
beams, beam position, truck (loading) position, and relative stiffness were considered. The
slab was modeled as rectangular and triangular isoparametric plate elements to account for
bending and no membrane stresses. The girders were discretized as beam elements to solely
include bending in a vertical plane. For verification purposes the mesh was refined using
elements half of the size of the originals, but the results varied within 1%, so it was
concluded the original mesh was small enough. Finally, a convenient and conservative chart
was developed to give lateral distributions factors for fatigue.
Brockenbrough (1986) used a parametric study using FEA to determine rational factors for
lateral distribution of live loads on composite curved I steel girder bridges. The model
consisted of QUAD4 shell elements, which include membrane and bending effects for the
concrete slab. For the girder web, BAR elements including axial and bending strains in two
directions as well as torsional effects were selected for the discretizing the flanges of the steel
girders and also for the crossframes, though for the latest it included the effects of the end
offsets and pinned joints. The interface between the top girder and the concrete deck was
modeled with rigid link (RBAR) elements to simulate the no slipping condition typically
developed at that location. For the boundary conditions, zero vertical displacement were used
at all the supports and zero horizontal displacements were used at the center supports. The
noteworthy aspect about this research is that the numerical model was in very close
agreement with the existing AASHTO formulation.
Bishara and Elmir (1990) used ADINA as the FEM software and considered three
components of the analysis: concrete deck, girders, and crossframes. The concrete deck was
discretized with triangular plate elements. The girders were divided in two parts: top and
bottom, each part being discretized with beam elements joined to the other half by steel link
elements. The top part was connected to the deck by constraint equations or rigid link
elements. The crossframes were also discretized as beam elements, but the stiffeners were
not included. The three simply supported multi-girder skewed bridges of 20, 40 and 60
17
degrees and the right angle bridge were subjected to a load scheme consisting of dead load
due to weight of slab, sidewalks and parapets, girders crossframes, and asphalt, and to live
load according to AASHTO(1) HS 20-44, which included truck load and lane load. Results
showed, that while in a non skewed bridge forces in the crossframes due to dead load are
tension for intermediate chords and compression for diagonals, on a skewed bridge these
transverse elements develop either compression or tension depending on the loading
condition. Furthermore, not only the higher the cross sections of the crossframes and the
skew angle the higher the forces developed on the crossframes but also the forces developed
on the end bent crossframes were insensitive to intermediate crossframe size changes.
Bishara (1993) carried out a parametric investigation whose main objective was to develop a
procedure for evaluating internal forces in intermediate crossframe members of simply
supported multi-girder steel bridges taking into account factors like skew angle, span length,
deck with, and spacing of crossframes. By means of a three dimensional finite element
discretization scheme of the system to simulate the interaction between all the elements and a
validation procedure using five multi girder bridges, it was possible to analyze 36 bridges
with the already mentioned geometrical configuration.
Using ADINA as the FEM software, and with some modifications to the scheme used by
Bishara and Elmir (1990) it was possible to model the system. Thin triangular plate elements
with six degrees of freedom per node were used to simulate the concrete slab. The girder
flanges were discretized as beam elements, the girder webs as shell elements, and web
stiffeners as truss elements. Rigid elements simulated the connection between the top flange
and the slab while crossframes were discretized using beam elements and bearings by means
of constraining degrees of freedom. Results obtained were very similar to those obtained by
Bishara and Elmir (1990).
Tarhini and Frederick (1992) conducted a parametric study to investigate the wheel load
distribution on steel bridges using ICES STRUDL II three dimensional finite element
18
analysis models subjected to static wheel loading. The parameters involved were the size and
spacing of the steel girders, presence of cross bracing, concrete deck thickness, span length,
single and continuous span, and composite or non composite behavior. The model consisted
of isotropic eight node brick element IPLSCSH, with three degrees of freedom at each node,
to model the concrete slab. The girder flanges and the web were discretized using three
dimensional quadrilateral four node plate element SBCR (shell element) to account for both
membrane and bending deformation properties.
Regarding the composite bridge action at the deck-flange interface, no releases were imposed
to those nodes at that location, therefore no slip was allowed. However, to simulate slip
typical of the non composite phase three linear springs were inserted at the interface nodes,
one on each 3D direction, whose stiffness was selected to allow the slab to move with respect
to the top flange. In the end, a new formula was developed to predict the wheel load
distribution as a function of the girder spacing and the span length that works for both
composite and non composite bridges.
Ebeido and Kennedy (1995) studied the influence of several parameters on the shear
distribution in skew composite steel – concrete bridges. These parameters were the angle of
skew, girder spacing, bridge aspect ratio, number of lanes, number of girders, end
diaphragms, and number of intermediate crossframes. The experimental studies involved six
simply supported skew composite steel bridge models. Each model was subjected to load at
various locations simulating truck loads. Deflections of steel beams, strains of beams and
slab, and reactions at the supports were measured. Three dimensional finite element
modeling of skew composite bridges was conducted, using ABAQUS as the computing
software. The reinforced concrete deck slab was modeled using a four node shell element
with six degrees of freedom at each node. The girders, end diaphragms, and intermediate
crossframes were discretized using three dimensional two node beam elements with six
degrees of freedom at each node.
19
While the two end supports were simulated using a boundary constraint option that restricted
the vertical displacements along the nodes at those locations, the multi point constraint option
was used between the shell nodes of the reinforced concrete slab and the beam elements
nodes on the girders. This was done to ensure full composite interaction, which is usually
done by means of the shear stud connectors. It was concluded, among other things, that the
results from the theoretical analysis were very close to those obtained on the lab tests.
Later on, Ebeido and Kennedy (1996) conducted an extensive parametric study of three
continuous composite skewed steel bridges. They were able to deduce empirical formulas to
determine span and support moment distribution factors for both interior and exterior girders
when subjected to full and partial dead and live (truck) loads. The results from lab tests
combined with a FEA were used to validate the models. Parameters like girder spacing, angle
of skew, bridge aspect ratio, spans ratio, number of lanes, number of girders, and
intermediate transverse diaphragms were considered.
The modeling process incorporated four node shell elements with six degrees of freedom at
each node to discretize the slab using ABAQUS as the software package. The longitudinal
girders and the transverse crossframes were modeled using a three dimensional two node
beam element with six degrees of freedom at each node. Intermediate supports and abutment
supports were modeled using specific boundary constraints, and with multipoint constraint
options (MPC) between the slab and the beam nodes on the longitudinal steel beams to
simulate full composite interaction. It was found that the exterior girder controls the design
of skewed bridges, as far as the span and support moments are concerned. One of the most
important findings is that the higher the skew angle, the smaller the span and support
moments of the girder, particularly when the angle is greater than 30°. It was also found that
transverse diaphragms moment connected to the girder improves load distribution on the
bridge.
20
In an effort to determine live load distribution on bridges with irregular plan geometries,
Tabsh et al. (1997) developed a methodology on which an isolated deck strip is loaded and
then analyzed as a continuous beam on elastic supports. The displacements and rotational
stiffness of the supports are computed based upon several parameters such as the girders
geometric properties, position of the truck wheels, etc. Finally the reactions from all strips
are transferred to the top flange of the girder in question to compute the girder distribution
factor as the ratio of the beam moment (or shear) due to the effect of the truck load divided
by two. The parameters considered were span length, continuity, number and spacing of
girders, bridge width, girder stiffness, and number of loaded lanes.
To verify the exactness of the aforementioned methodology a three dimensional finite
element analysis was implemented using the computer program ANSYS. It involved the use
of three different elements to model the entire system. To discretize the top and bottom
flanges two node three dimensional beam elements with six degrees of freedom at each node
were selected. The steel web and the concrete deck were idealized with four node rectangular
shell elements with six degrees of freedom at each node in order for plane membrane and out
of plane bending effects to be computed. For the crossframes and diaphragms, three
dimensional beam elements were considered and rigid three dimensional beam elements
were used to connect the centroids of the top flange steel beam elements to the centroids of
the slab elements. The verification of the model was part of the work by Sahajwani (1995).
SAP 90 and ICES-STRUDL II were the computer software Mabsout et al. (1997a,
1997b,1998) used when they carried out an investigation to assess the degree of accuracy
and the performance of four different finite element modeling techniques of common use in
evaluating the wheel load distribution factors of steel girder bridges. The first model
consisted of quadrilateral shell elements with five degrees of freedom per node for the
concrete slab and space frame elements with six degrees of freedom per node for the girders.
The centroid of the concrete deck coincided with the centroid of the girder cross section. For
the concrete deck, the second finite element model considered the use of quadrilateral shell
21
elements and eccentrically connected space frame members representing the girders, while
rigid links were imposed to account for the eccentricity of the girders with respect to the slab.
The third model included the idealization of the concrete slab as well as the steel girder webs
by means of quadrilateral shell elements, while girder flanges were discretized as space
frame elements and flange to deck eccentricity was modeled by imposing rigid links.
Isotropic eight node brick elements with three degrees of freedom at each node were used on
the fourth model to idealize the concrete slab and quadrilateral shell elements for discretizing
the steel girder flanges and webs. Results indicate that when dealing with non skewed
bridges the use of quadrilateral shell elements for modeling the concrete deck and concentric
space frame elements for modeling the girders is encouraged.
Samaan et al. (2002) carried out a parametric study to evaluate the load distribution of sixty
continuous two span composite concrete slab-steel spread box girder bridges using ABAQUS
as the FEM software. Several parameters were considered such as span length, number of
spread boxes, number of lanes, and number of cross bracings. All the models were subjected
to eleven loading conditions. The models used, previously verified by Sennah and Kennedy
(1998, 1999), were analyzed with four node shell element S4R with six degrees of freedom at
each node for the concrete slab, steel girder webs, bottom flanges, and end diaphragms. This
element could account for membrane, bending, and torsional effects. A 3D two node beam
element B31H was adopted to model top flanges, cross bracings, and top chords. The
composite behavior between the slab and the top flange, due to the shear studs, was modeled
by using multi point constraints MPC on the interface nodes. The bridge supports were
modeled by constraining both vertical and lateral displacements at the lower end nodes of
each web located at the end supports, whereas all displacements were restrained at the
support on the mid span. The outcome revealed that current practices were either too
conservative or too under predicting.
In an effort to determine the accuracy of the numerical methods for predicting the response
of skewed bridges during construction, Norton et al (2003) developed two different models.
22
The first model was a 2-D grillage on STAAD/Pro, in which the girders were modeled as non
composite frame elements and wet concrete was considered as uniform loads acting along
each girder, and applied in four stages to account for the pouring sequence and to simulate all
the components of the system, such as self weight of the girders, weight of wet concrete, and
point loads from the screed supports. The second model was a 3-D finite element model
constructed and analyzed on SAP2000. The modeling process included shell elements for the
girder webs while space frame elements were used to model girder flanges, stiffeners, and
crossframes. Boundary conditions included restrictions on the translations in the three
directions of the bottom node of the girder webs at the supports and restrictions on the
vertical and lateral translation only. The crossframes were rigidly connected to the girders
while accounting for non composite behavior of the concrete deck by assigning a modulus of
elasticity of 68.9 MPa to the shell elements of the deck.
The Finite Element procedure has always been a rational way to deal with cumbersome and
complicated systems. This is the case of Fu and Lu (2003) in the development of a Finite
Element Model to simulate the composite deck girder interaction. The girders were
discretized with traditional eight-node isoparametric quadrilateral elements, though the
flanges of the girder were modeled using plate elements and the web with plane stress
elements. As for the shear studs, bar elements were used to provide a dimensionless link
between the deck and the top flange of the girders. With the help of the computer program
RESIDU and with the results from previous experimental studies (Yam and Chapman 1972)
the numerical model was evaluated. The results were compared to those obtained using
classical transformed area method. The numerical results yielded values that were very close
to the experimental but considerably far from those obtained with the transformed area
method.
Huang et al. (2004) conducted research to develop a better understanding of the transverse
load distribution for highly skewed steel girder bridges by means of both numerical and
experimental analysis. The field test was conducted to measure strains at different points
23
along a 60 degree skewed bridge when two fully loaded trucks pass over it, following a
particular load scheme. The analytical model consisted on a three dimensional FE model
using ANSYS as the software package. Four node three dimensional elastic shell elements
with six degrees of freedom per node were used to model the concrete slab and the girders
while the crossframes were modeled with two node three dimensional elastic beam elements
with six degrees of freedom per node. For both the end supports boundary constraints were
imposed in which the translational displacements were restricted except for the longitudinal
direction. However, for the intermediate pier support all the displacements were restrained.
No rotational constraint was considered. The overhangs and parapets were ignored. The end
results showed that AASHTO LRFD formulation for live load distribution tends to be safely
conservative for positive bending and for negative bending they are accurate but not
conservative.
The research by Chung and Sotelino (2005) was focused on evaluating the behavior of
composite steel girder bridges using FEM, including non linear behavior with the ABAQUS
software. Flexible shell elements were used to model the deck. The 8 noded Mindlin layered
shell elements (S8R) were selected due to its improved ability to model the non linear
behavior that occurs on the failure mechanism of concrete, including crack propagation
through the slab thickness and dowel effect. The girders were modeled using Timoshenko
beam elements (B32) to eliminate potential incompatibility on the boundaries, and for
modeling the bearings spring elements with displacement constraints were selected. To
model composite action between the girders and the deck rigid multi point constrained
elements (MPC) were used to connect the centroid of the girder cross section and the mid
surface of the slab. The models were verified by means of two experimental studies done by
Jofriet and McNiece (1971) and Kathol et al. (1995). The predicted and actual results were in
close agreement, with a 10% difference.
Choo et al. (2005) studied the effects of variables such as environmental and material and
concrete placement on the response of a skewed High Performance Steel (HPS) girder bridge
24
during the construction stage. Temperature changes during the pour and forces developed
during the setting of concrete are among the most important parameters considered in the
study, along with the comparisons between stresses on the exterior girders in terms of the two
possible concrete pouring schemes. A numerical investigation was also conducted to carry
out the parametric study, and SAP2000 was selected as the computer program for the finite
element analysis. The girders were modeled with four node shell elements and the wet
concrete was idealized by a combination of three and four node shell elements in order to
accurately distribute the loads to the girders. They were modeled in this manner because deck
stresses were not in the scope of the investigation. The connection between the deck and the
girders was guaranteed by using rigid links, and the crossframes were modeled with three
dimensional frame elements. To validate the model stresses from the FEA were compared to
those obtained from instrumentation in the field (strain gauges). Boundary conditions,
temperature effects, and concrete stiffness were studied in detail. They concluded that time
dependant concrete modulus effect was negligible when determining the stresses on the
structure but temperature changes were of paramount importance. It was also found that the
best concrete pouring sequence for simply supported skewed bridges was that with the screed
parallel to the supports.
Beckmann and Medlock (2005) used a scale model with girders made out of poster board to
make them flexible enough to be able to measure both rotations and translations at the girder
ends. Various AASHTO/NSBA issues were addressed such as the fact that ends of girders do
not develop in plane rotations for different bearing alignment conditions. They also
developed expressions to determine transverse movements and account for possible ways to
deal with design problems like those mentioned in the AASHTO/NSBA G 12.1-2003
Guidelines for Design for Constructability. It was found that the ends of the girders will
rotate about an axis that runs through the centerlines of rotation at the bearings, and do not
rotate in a vertical plane parallel to the girder web, as it was assumed initially. The transverse
movement of the top flange relative to the bottom flange results in the ends of the girders
being out-of-plumb. This condition has a direct effect on the position (deflection, twist, etc.)
25
of the girder webs at intermediate crossframes where there is differential deflection between
adjacent girders due to their relative locations in the span.
2.2.4 NCSU / NCDOT Related Studies
Whisenhunt (2004) measured deflections on five different skewed steel girder bridges during
the construction phase in order to determine the real non-composite deflection behavior of
the bridge and compare it to the behavior predicted by the current design methodology. The
current design procedure involves computing deflections in each girder as though they
worked independently or as single units. It was found that quantifying deflections by such a
procedure turned out to not only be inaccurate by an average of 38 % on interior girders or
around 6 % on exterior girders, but also it does not incorporate transverse distribution of
loads along the crossframes and diaphragms that interconnect the girders.
To make up for these discrepancies, a three dimensional finite element analysis was
conducted using ANSYS as the computing platform including parameters such as bridge
skew, cross-frame stiffness, stay-in-place (SIP) metal deck forms, and partial composite
action. The results from these studies were then compared to those obtained from the field
and from the current design formulation. It was found that they significantly improved the
accuracy of the predicted deflections (within 6 to 14%) and even accounted for the
considerable effects of the SIP metal deck forms on the torsional stiffness and the overall
behavior of the structure.
The objective of the research conducted by Paoinchantara (2005) was to develop a simplified
modeling method to predict the non-composite dead load deflections of the steel plate bridge
girder. The study was conducted in order to create a simplified modeling method for both
single span and two-span continuous bridges including parameters such as bridge skew,
cross-frame stiffness, and stay-in-place metal deck forms using SAP2000 as the primary
finite element software. By measuring the deflections in the field during the construction the
26
actual non composite deflection behavior of the bridge was determined and compared to the
results from modeling. Four simplified models were included in the research, which included
a 2D grillage model, a three dimensional analytical model which included frame elements as
the crossframes, another three dimensional model including the SIP forms as frame elements,
and a three dimensional model where the SIP forms were discretized as shell elements. As a
result, the predicted deflection of the simplified models agreed well with the measured
deflections and results from finite element models results for the single span bridges, whereas
the predicted deflections from the simplified models did not agree with the measured results
for the two-span continuous bridge. It was also concluded from both field measurements and
modeling results that, on one hand stay-in-place metal deck forms have a significant effect on
the non-composite dead load deflection behavior, and on the other hand that composite action
has a slight effect on the vertical deflection behavior for skewed steel plate girder bridges.
Fisher (2005) carried out research to develop a simplified procedure to predict dead load
deflections of skewed and non-skewed steel plate girder bridges. This was done by studying
five bridges following Whisenhunt's (2004) approach of discussing bridge descriptions, field
measurement techniques, and measurement results while increasing the variance in both
bridge type and geometry to provide additional data for the validation of the finite element
models. Using ANSYS as the FEM platform and MATLAB as the preprocessor program
software, it was possible to carry out the numerical analysis including an extensive
parametric study that was conducted to investigate the effect of skew angle, girder spacing,
span length, crossframe stiffness, number of girders within the span, and exterior to interior
girder load ratio on the girder deflection behavior.
With the results from the parametric study it was concluded that the simplified procedure
may be utilized to predict dead load deflections for simple span steel plate girder bridges. An
alternate prediction method was proposed to predict deflections in continuous span steel plate
girder bridges with equal exterior girder loads. Additional comparisons were made to
validate this method.
27
2.2.5 Need for Research
Is it possible to quantify the extent of lateral flange bending of steel plate girders in heavily
skewed bridges? Could a methodology for predicting the magnitude of lateral translation be
developed? Provided the answers for the aforementioned questions are positive, is it possible
to propose suitable mitigation strategies?
Whatever the answers are, the AASHTO 2003 guideline for design for construction has
addressed this fact and there is a limited amount of literature available that documents in
detail construction issues of steel plate girder bridges such as differential deflections between
adjacent girders, out-of-plane girder rotations, and problems that occur during staged bridge
construction. Discrepancies researchers have documented related to predicting structural
behaviour during bridge deck construction are addressed in moderation in literature. What is
more, only a few investigators have dealt with the problem of how to control the lateral and
transverse deformations a skewed bridge undergoes during the non composite stage during
the erection and construction phase, including effects of the overhang falsework loads on the
outer girders.
Parametric studies have included issues related to the skew angle, crossframe stiffness, girder
spacing, span length, influence of SIP metal deck forms, and torsional and lateral stiffness /
strength. These variables have been identified as some of the factors to have great influence
on the skewed bridge behavior.
Numerical modelling has also been one of the researcher‟s major and most helpful tools,
particularly those that rely upon three dimensional finite element modeling and analysis.
Numerous methods have been reviewed and considered to develop a procedure and
methodology that would be suitable for this research. As in previous research conducted by
Helwig (1994), Egilmez et al. (2003), Helwig and Wang (2003),Whisenhunt (2004) and
28
Fisher (2006) the methods that were developed and implemented in those investigations have
been identified as the basis for the finite element modelling used in this research.
It is intended that throughout the investigation conducted herein, to not only answer the
questions already generated, but to obtain a better general understanding of the skewed
bridges by increasing current knowledge of the lateral flange bending behavior of steel plate
girders.
2.3 Field monitoring of steel girders during placement of the bridge deck.
This task was carried out on a moderate skew steel bridge located on Chicken Road over a
construction segment of US 74 between Maxton and Lumberton, and a heavily skewed
bridge located over Roaring Fork Creek in the mountain region of north western North
Carolina. Rotations and strains were monitored on both of these bridges to determine the
lateral translation of the girder flanges due to lateral flange bending. The girders were
instrumented to measure the rotations on both the web and bottom flanges at quarter points
along the span of the girders. Measurements were recorded at various stages of the deck
placement to capture the response of girders throughout the deck construction.
2.4 Analytical investigation and quantification of lateral flange bending.
An analytical investigation was conducted to quantify the lateral flange bending of steel plate
girders in heavily skewed bridges. More than 180 three-dimensional finite element models
were developed for each of the bridges monitored in the field. The field measurements were
used to validate the finite element models. Once the validation study was completed
additional models were created with the help of a computational program specifically
developed for this research to simulate the effects of numerical parameters like exterior to
interior moment of inertia (strong axis) ratio, exterior to interior load ratio, number of
girders, number of transverse stiffeners, number of crossframes, crossframes stiffness, stay in
place forms stiffness, and spacing to span ratio. Additionally non numerical parameters like
29
crossframe type, crossframe layout and pouring sequence were also considered. The finite
element simulations were used to quantify the lateral flange bending effects due to the out of
plane torsional rotations and the overall behavior of the possible locked-in stresses during the
construction stage. Particular attention was given to the modeling of the bridge crossframes,
end-bent diaphragms, and support bearings.
2.5 Development of mitigation strategies
From the extensive parametric analysis it was possible to classify the effects each parameter
had on the entire structure. This allowed quantifying the potential benefits or harms each of
them poised on the overall rotational behavior of the girders. The effects of the numerical
parameters were classified as favorable, neutral, or unfavorable with respect to the original
structure.
30
CHAPTER 3. FIELD MEASUREMENTS
3.1 General
As part of the investigations related to characterization of lateral flange bending on skewed
steel girder bridges it was necessary to obtain real time information generated during the
construction process. The lack of available literature related to cross section rotations on
skewed bridges made the investigation even more challenging.
The field measurement process started by establishing the range of required geometrical
conditions of the bridges that were considered ideal for the purpose of the investigation.
Whisenhunt (2004) and Fisher (2005) suggested that the best results are obtained for skew
angles greater than 20 degrees. Then from the available alternatives two bridges were
selected that met the established criteria. Finally, transverse rotations and deflections at
quarter points and supports were selected as the primary measurement variables to be used on
the field. Temperatures during the construction process were also considered.
3.2 Bridge Selection
As it was mentioned before, the first step was to select the bridges to be monitored during the
construction process. To carry out such a task it was required to single out bridges that
comply with certain geometrical constraints in order to ensure the adequate and reliable
nature of data generated. These selection criteria included skew angles less than or equal to
45 deg, simple spans, four or more girders, and girder spacing between six and ten feet. Table
3-1 has all the available bridges that could be included in the investigation, provided by the
NCDOT.
31
Table 3-1. List of potential bridges to be included in the study (source: NCDOT)
3.3 Bridges Studied
3.3.1 General Information.
There are some characteristics shared by the two bridges included in the analysis, such
as:
Steel plate girders were connected either by K-type cross-frames or by Diaphragms
Elastomeric bearing pads: deformations at these locations were considered as part of
the investigation
All bridges were fabricated with AASHTO M270 steel. One of them was grade 50
and the other was grade 345W.
Design phase included the differential deflection procedure to determine the required
camber of the girders.
3.3.2 Bridges Monitored
Table 3-2 presents part of the geometric parameters included for each bridge. The reason
they were selected was not only because the met the selection criteria but their
Project Location TIP #Skew
Angle
Equiv.
Skew
Angle
# of
Spans
Simple vs.
Cont.
Girder
SpacingOverhang
Girder
Spans
# of
Girders
On SR 1320 (Roaring fork Rd) over Roaring
Fork Creek.B-4013 23 67 1 Simple 6'-6'' 1'-1.5'' 85' 5
SR 1309 (Lower Alarka Rd) over Alarke Creek B-3701 140 50 1 Simple 6'-6'' 2'-7.5'' 100' 5
SR 1003 (Chicken Rd) over US 74 between SR
1155 & SR 1161R-513BB 136 46 2 Simple
9'-10"
(3.0m)varies
133' (40.4m),
125' (38.2m)4
SR 1155 (Dew Rd) over US 74 R-513BB?
US 70 over Norfolk Southern RR between SR
1739 and NC 801R-2911D 32 58 1 Simple 8'-0" 3'-7.5" 160' 5
SR 1331(Little River Church Rd) over Grassy
CreekB-4005 50 40 1 Simple 9'-7" 3'-9" 122' 4
SR 1446 (Linney's Mill Rd) over Rocky Creek B-4006 49 41 1 Simple 9'-0" 3'-9.5" 120' 4
32
construction date was found to be within a period of six months, which met the time
constraints for the investigation
Table 3-2 Summary of bridges
Bridge Span
(ft)
Number of
Girders
Skew angle
(deg)
Spacing
(ft)
Crossframe
type
Chicken Rd 133 4 137 10 K-type
Roaring Fork 73.5 5 23 6.5 Diaphragm
Following is a brief description of the bridges selected for this study.
3.3.3 Bridge on SR 1003 (Chicken Road) over US 74 between SR 1155 & SR 1161 in
Robeson County. Project # R-513BB
Chicken Road Bridge is a two single span, four girder bridge. It is located over a construction
segment of US 74 between Maxton and Lumberton. Both spans are almost identical with the
only difference of a few inches and a few fractions of a degree in skew because the bridge
was located on a slight curve along the road (the maximum superstructure arc offset is 7 in).
For this reason both spans produced similar results and therefore only those from one of the
spans will be presented. Deflections and rotations on both flanges and the web were
monitored at quarter points along the girders as well as at the end bents to mesure support
settlements. At the end bents rotations were only monitored on the bottom flanges and web.
The presence of formwork made the top flange unreachable. The pouring phase started close
to midnight on one end bent and finished close to 9:00 am. on the other bent. A general view
of the bridge is presented on Figure 3-1. All the geometrical properties of the bridge as
wellas material information is presented on Appendix B.
33
Figure 3-1. Chicken Road Bridge
3.3.4 Bridge No 338 over Roaring Fork Creek on SR 1320 (Roaring Fork Road) in Ashe
County. Project # B-4013
Roaring Fork Bridge was located in the mountain region of north western North Carolina. It
is a five girder simple span bridge and the most outstanding feature is that it has a severe
skew angle of 23 deg. (See Figure 3-2). The bridge spans across a creek so the typical quarter
point locations for monitoring were compromised. Therefore deflections and rotations were
only monitored at end bents and mid points.
Similar to what occurred on Chicken Road Bridge, rotation measurements were limited to
bottom flange and web at the end bents due to constraints associated to the formwork. The
concrete was cast during a five hour period of time. Appendix C presents the most important
geometrical and material information for this bridge.
34
Figure 3-2. Roaring Fork Road, in Ashe County
3.4 Field Measurements
3.4.1 Overview
The primary purpose of the investigation was to monitor girder cross section rotations at a
given location. Nevertheless, in order to have sufficient data to validate the procedure it was
necessary to measure deflections at some points along the span. All the information regarding
35
how those deflections were determined using string potentiometers, dial gauges, or the
alternate procedure can be found in the Whisenhunt (2004) and Fisher (2005) investigations.
3.4.2 Girder Cross Section Rotations.
A digital level with a precision of 0.1 degrees combined with a carpenters level were the
main instruments used to monitor rotations along the span.
First the carpenter‟s level was placed against the element (i.e: the bottom flange or web) to
be measured. The digital level was then placed against the carpenters to determine the
corresponding rotation in degrees, as shown on Figure 3-3
Figure 3-3. Procedure to measure rotations on the Bottom Flange (left) and Web (right)
Due to the existence of different constraints such as the stay in place forms, re-bars, etc. the
top flange rotations were measured from the lower side at those locations where it was
possible to access the top flange area and using the level directly on the steel element (See
Figure 3-4).
carpenter’s level
Digital Level
Girder web
web
carpenter’s level
Digital Level
Girder web
Girder bottom flange
36
Figure 3-4. Procedure to measure rotations on Top Flanges
3.4.3 Temperature
Besides the typical deflections and rotation readings it was important to keep track of the
temperature changes during the concrete cast. To do so, an infrared thermometer was used to
measure temperature changes on the structure. It is noteworthy the fact that for steel
structures temperature changes have a major impact of the structural behavior. For a typical
bridge, changes of more than 70° F are possible in a period of 24 hours and this changes may
produce stresses and deformations that must be accounted. However, it was found that during
the construction process of both bridges the largest recorded change in girder temperature
was 10° F, which could be considered negligible as far as the structural effects it can lead to.
3.4.4 Sign Convention
The sign convention used for all the field measured rotations was as follows: following the
direction of the span, this is from end bent 1 towards end bent 2, positive rotations are
clockwise. Figure 3-5 presents a schematic of this condition.
Figure 3-5. Directions of positive rotations
Digital Level
Girder web
Girder top flange
End Bent 1
Span
Positive Rotations
37
3.4.5 Sources of Error
It is worth mentioning that the reason to use the carpenters‟ level is that flanges and webs are
not 100% flat. In an effort to capture the real behavior it was necessary to “average out” the
rotation measurements. The carpenter‟s level covers almost all the web height and all the
bottom flange width for both of the bridges studied, hence the values reported were the
average rotations of the section (see Figure 3-6 ).
Figure 3-6. Imperfections of the straightness
3.4.6 Limitations
On most of the top flange locations access was severely compromised due to the different
construction components located along the span. On Chicken Road Bridge there were several
wood studs along the span used to control rotations during the construction process. On
Roaring Fork Road Bridge the stream flow was particularly strong which made top flanges
along the span impossible to reach. For this same reason on Roaring Fork only values at the
end bents and mid span could be monitored.
3.5 Summary of Acquired Field Data
On Table 3-3 the different rotation can be found in degrees recorded for the two bridges
included on this research. It is worth mentioning that these values represent the total rotations
gap
Slightly crooked web & flanges
38
measured when all the concrete was poured. Additional information with regards to
deflections can be found on Appendices B and C.
Table 3-3. Summary of girder rotations, in degrees, recorded for both bridges
G1 G2 G3 G4 G5Top Flange - - - - -
Web -0.6 -0.6 -0.7 -0.7 -
Bottom Flange -0.6 -0.3 -1.1 -0.5 -
Top Flange - - - - -
Web -0.3 -1.2 -0.7 1.2 -
Bottom Flange 0.1 0.3 0.5 0.7 -
Top Flange - - - - -
Web 0.5 0.2 0 -0.2 -
Bottom Flange -1.4 -0.3 0.1 -1 -
Top Flange - - - - -
Web 0.9 0.4 0.5 0.2 -
Bottom Flange -1.6 -0.6 -0.8 -0.6 -
Top Flange - - - - -
Web 0.6 0.7 -0.7 0.5 -
Bottom Flange -0.4 -0.4 0.2 -0.2 -
Top Flange - - - - -
Web -0.1 -0.2 -0.3 -0.4 0
Bottom Flange 0.6 0.1 0 0.1 -0.7
Top Flange - - - - -
Web - - - - -
Bottom Flange - - - - -
Top Flange 0.8 -2.7 -1.7 0.6 0
Web -0.3 -0.4 -0.2 -0.2 -0.2
Bottom Flange -5.3 0.4 0.3 0.1 -1.3
Top Flange - - - - -
Web - - - - -
Bottom Flange - - - - -
Top Flange - - - - -
Web 0.7 1 0.4 2.3 0.1
Bottom Flange -0.9 -0.9 -0.8 -0.3 -0.1
Second End Bent
GirderBridge Loc Section
Chicken Road
(Span A)
Roaring Fork
First End Bent
First Quarter
Mid Span
Third Quarter
Second End Bent
First End Bent
First Quarter
Mid Span
Third Quarter
39
CHAPTER 4. FINITE ELEMENT MODELING
4.1 Introduction
Previous research, done by Whisenhunt (2004) and Fisher (2005), has demonstrated the
powerful abilities of this program. The purpose of the modeling process is not only to
compare field measurements with those obtained with the finite elements, but to be a tool
used to predict behaviors in situations in which the numerical and non numerical parameters
are modified.
Special attention will be given to those bridge components that were not part of the
investigations of Whisenhunt (2004) and Fisher (2005). To reduce the computational cost of
model generation, a preprocessor program was developed in Visual Basic 6.0 to automate the
procedure of creating the models varying the corresponding parameters.
4.2 General
Typically for the steel girder design process during the non composite phase only linear
elastic behavior is considered and static forces are the common loading case. Hence, only
static, linear elastic analysis was considered throughout the investigation. Throughout this
section there will be a brief description of the bridge components as well as a summary of the
modeling procedure and its evolution.
4.3 Bridge Components
Most of this investigation was based on findings and theories used in previous research by
Whisenhunt (2004) and Fisher (2005). In an effort to be as concise as possible many of the
bridge component descriptions were not included in this dissertation and can be found in the
aforementioned investigations. However, special attention will be given to those bridge
components that were required to be modified to accommodate the rotations studied herein.
40
4.4 Crossframes
As far as the investigation is concerned two types of end bent crossframes and three different
types of intermediate crossframes were included in the analysis.
4.4.1 End Bent Crossframes and Diaphragms
End bent crossframes were used on Chicken Road Bridge whereas diaphragms were used for
Roaring Fork Bridge. Figure 4-1 illustrates both the end bent crossframes and diaphragms.
Regarding the modeling procedure, both the top channel and the diaphragms were modeled
using SHELL93 type of elements. These are eight noded isoparametric shell elements that
have been proven to be the most accurate and reliable type of element when it comes to
modeling typical steel sections. This is due to not only their inherent ability to transfer shear
forces within its plane, but to the possibility of accommodating flexural deformations along
their span. A four noded element would be too stiff. The WT sections were still modeled with
BEAM 4 and LINK8 elements.
End Bent Crossframe (Chicken Road Bridge) End Bent Diaphragm (Roaring Fork Bridge)
Figure 4-1. Both types of end bent crossframes considered
It is worth recalling that BEAM4 elements are capable of transferring forces and moments
across its span and are defined with two or three nodes with six degrees of freedom each. On
CHANNEL
GUSSETPLATES
GUSSETPLATES
WT SECTIONS
BOLTS
MC SECTIONBOLTS
GUSSETPLATES
41
the other hand LINK8 elements are typically used to model those components that only
transfer axial force, such as diagonals of a truss, etc. They are defined with two nodes with
three degrees of freedom.
Besides the struts and diagonals, the gusset plates were also included in the modeling
procedure in an effort to enhance the response of the structure. Similar to the sections already
mentioned, SHELL93 elements were used in the modeling process, and the connection
constraints imposed by the bolts were included. This was possible by coupling the bolt
locations on the gusset plates with those on both the stiffeners (or connectors) and the
channel. Figure 4-2 depicts such a condition.
Figure 4-2. Coupling of nodes at bolt locations to simulate real interaction
4.4.2 Intermediate Crossframes
As mentioned before, three different types of intermediate crossframes were considered,
although two of them were used on the actual bridges. The K-type and X-type crossframes
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Coupled nodes atbolt locations on
the channel Coupled nodes atBolt locations on
the Stiffeners
42
were modeled exactly as Whisenhunt (2004) and Fisher (2005) did. However, the
diaphragms were modeled as the end bent diaphragms previously mentioned, using
SHELL93 type of elements and coupling the nodes at the bolts locations with the
intermediate stiffeners (or connectors) and using independent thicknesses for the web and the
flanges. Figure 4-3 shows an illustration of these three types of crossframes.
K-type X-type
Intermediate Diaphragm
Figure 4-3. Three types of intermediate diaphragms or crossframes
4.4.3 Elastomeric Pads
One of the new features included in this investigation was the incorporation of elastomeric
pads at the end bents since both bridges were supported on this type of bearing. To achieve a
reasonable approach, SOLID186 elements were selected to simulate the effect of the
elastomer. This higher order 20 node isoparametric solid element has the particular property
INTERMEDIATE STIFFENERS
ANGLES BOLTS
INTERMEDIATE STIFFENERS
ANGLES
BOLTS
MC SECTIONBOLTS
INTERMEDIATECONNECTORS
43
of exhibiting a quadratic displacement behavior, which allows it to depict deformations of the
pad with a high degree of accuracy. The material properties, which include shear modulus
and poissons ratio, were studied by Muscarella and Yura (1995). Although the type of
connection between the elastomer and the concrete was constrained by “pins” or “rollers”,
depending on the end bent, this study did not take into account variations of the material
properties nor the actual support condition which essentially relies on friction between
concrete and the elastomer and between the steel and the elastomer. Nonetheless, stresses
were checked at those locations using Von Mises theory and in no case were they close to the
yielding value. The maximum stress measured on these regions was in the range of 15% of
the yielding stress.
Additionally, rigid links were used to connect the sole plate with the bottom flange of the
girder. This was done to simulate the eccentricity due to the thicknesses of both the plate and
the bottom flange, which can be up to 3 inches. This was possible with the MPC184 rigid
element. This element only requires two nodes to be defined. A picture with the boundary
conditions is shown on Figure 4-4.
Figure 4-4. Constraints at the supports
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Pin constrains at the supports
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4.5 Modeling Procedure
4.5.1 Initial Model (Model 1)
The first approach to the problem was to consider the original model developed by
Whisenhunt (2004) and Fisher (2005). This particular model had the ability to accurately
predict deflections along the span for steel skewed bridges. However, there were two
conditions that needed to be re-evaluated.
One condition was the possible sources of error induced in measuring rotations due to the
lack of part of the components, such as the Stay In Place (SIP) forms on the region between
the end of one girder and the same end of the adjacent girder. The other condition was the
fact that none of the original models account for diaphragm type of frames and the
mechanism by which these diaphragms transfer forces which is different than those on the
crossframes. In consequence it was necessary to enhance the original model including those
components that were required (SIP forms) and modify those that could be improved
(Crossframes). Figure 4-5 shows how the SIP‟s are not included on the end regions.
Figure 4-5. Girders end regions on Model 1
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To capture the effect of the empty SIP region on the overall behavior of the bridge trial
loading cases were carried out such that forces along the SIP‟s were recorded on one of the
bridges. Figure 4-6 shows an example of those forces between an exterior girder (G1) and its
adjacent girder (G2). It is clear that at no locations along the span, SIP forces reach the value
of 1 kip, and most of the force is carried by the diagonal elements. The dotted lines represent
an outline of the plan view of the bridge between the exterior girder 1 (G1) and its adjacent
girder 2 (G2). It can be seen that no forces are developed in the initial region of G1 and the
final region of G2.
Figure 4-6. SIP force distribution along the span
To determine the reliability of the model, the next step was to incorporate the SIP forms
along those initial and final regions and measure the affect of such a modification.
4.5.2 Next Model (Model 2)
One of the challenges related to the incorporation of the stay in place elements in the final
regions was the gap created between the end of the SIP‟s and the end bent diaphragms. In
order to solve this situation it was necessary to link the SIP forms to the diaphragms with
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 200 400 600 800 1000 1200
FOR
CE
(kip
)
SPAN (in)
SIP FORCES BETWEEN G1 AND G2 (MODEL 1)
STRUT DIAG 1 DIAG2
G1
G2
46
rigid element connectors. These elements allow the diaphragms to lock the ends of the SIP
forms into themselves creating a particular connection in which no deformations occur along
the connectors while the eccentricity between the end nodes of these elements accounted for
the torsional component transferred into the end bents.
Although the lengths of the SIP‟s in this region are notoriously shorter, no adjustments were
made to the cross sectional area for either the struts or the diagonals to preserve the same
properties that the rest of the SIP‟s have. The purpose behind it was to determine how
dependent the force distribution along the SIP‟s to the overall stiffness was. Figure 4-7
presents the new model incorporating the new elements.
Figure 4-7. Second model detail, incorporating SIP's on the end regions
Similarly to the original model, the forces developed on these SIP elements were monitored
and the results presented in Figure 4-8.
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Figure 4-8. Force distribution along the SIP's in Model 2
It can be noticed that the magnitude of the SIP forces in the end regions are particularly
smaller than the rest of the structure. Although the results may not agree with the higher
stiffness values for the SIP forms in the end regions, they should have led to higher forces. It
is also a fact that the end bent diaphragm stiffness is even higher than the SIPs and therefore
most of the forces developed in that region should be absorbed by these diaphragms. Figure
4-9 shows how the lateral forces are distributed between the SIP forms and the crossframes
or diaphragms. It can be seen that he relative value of lateral forces between these two
components can be in the order of 8 to 1.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 200 400 600 800 1000 1200
FOR
CE
(kip
)
SPAN (in)
SIP FORCES BETWEEN G1 AND G2 (MODEL 2)
STRUT DIAG 1 DIAG2
G
1
G
2
48
Figure 4-9. Force distribution between SIP's and Crossframes
Although Model 2 seems to be more appropriate, there is still a requirement to enhance the
crossframe components. The reason is shown in Figure 4-10. It can be seen that the rotation
values for both models are exactly the same, so a good way to approach the problem was to
substitute the 2D end bent BEAM4 elements for a 3D structure based on SHELL93 elements.
0
2
4
6
8
10
12
14
0 200 400 600 800 1000 1200
FOR
CES
(ki
p)
SPAN (in)
SIP & XF FORCES BETWEEN G1 AND G2
STRUT DIAG 1 DIAG2 X FR
IntermediateCross Frames
G1
G2
49
Figure 4-10. Rotations comparison between Models 1 and 2 at Top Flange
The new model should be able to account for the rotational constraints imposed at the
connections between the end bent stiffeners and the diaphragms. Additionally, in order to
generate a more realistic model these constraints should be located at the connection bolts.
4.5.3 Model 3. An improved discretization
A higher order approach was considered to assemble the new model of the bridge. For this
case the end bent diaphragms and the intermediate diaphragms were modeled using
SHELL93 elements and connected to the stiffeners at the bolt locations (Figure 4-11). This
-0.150
-0.100
-0.050
0.000
0.050
0.100
G1 G2 G3 G4 G5
RO
TATI
ON
(D
EGR
EES)
GIRDER
ROTATIONS AT TOP FLANGE
INITIAL
MIDSPAN
FINAL
-0.150
-0.100
-0.050
0.000
0.050
0.100
G1 G2 G3 G4 G5
RO
TATI
ON
(D
EGR
EES)
GIRDER
ROTATIONS AT TOP FLANGE
INITIAL
MIDSPAN
FINAL
MODEL
MODEL
50
was possible by coupling the nodes on the diaphragms to the corresponding nodes on the
stiffeners as previously depicted on Figure 4-2.
Figure 4-11. Model 3 including diaphragms discretized with shell elements.
With this improved version of the bridge it was possible to carry out a preliminary study to
determine whether there was any correlation between the skew angle and the maximum
deflections on the bridge. Although this analysis was not necessarily related to rotations it
could give an excellent insight of the systematic behavior of the steel skewed bridges.
Several different skew angles were considered ranging from 15 deg to 90 deg. The results are
plotted in Figure 4-12.
The good correlation between the skew angle and deflections leads to think that there is some
type of systematic behavior on skewed bridges and the skew angle seems to play a major role
on the behavior of these structures.
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Figure 4-12. Relationship between skew angle and maximum deflections
4.5.4 Model 4 Final Model
The most important objective throughout the investigation was to accurately predict the
torsional rotations of the girders. It was mandatory to include all the structural components in
the finite element model. Figure 4-13 presents what the final finite element model considered
in these investigations.
In order to account for the effects of the gusset plates on the overall behavior of the structure
it was essential to include the necessary components in the model. So that rotations would be
more accurately predicted consideration of a more real set of constraints imposed on the end
bents such as those imposed by the bolts was necessary. To impose such constraints the
gusset plates were modeled using SHELL93 elements and the previous geometry of the
diaphragms were modified such that they fitted the new configuration.
y = - 0.001x2 + 0.0785xR² = 0.9996
0
0.5
1
1.5
2
2.5
0 10 20 30 40 50 60 70 80 90
MA
X D
EFLE
CTI
ON
(in
)
SKEW ANGLE (DEG)
SKEW ANGLE VS. DEFLECTION FOR ROARING FORK BRIDGE
52
Figure 4-13. Detail of the end bent connection in the final model (Model 4)
4.5.5 Validation of Results.
In this section results from all four models are presented and compared in an effort to
validate their accuracy and reliability. Both deflections and transverse rotations were used as
evaluation criteria. Figure 4-14 presents the results for the four models and the field
measurements for both deflections and transverse rotations in one of the bridges. It can be
noticed the evident difference between rotations on model 4 and the rest of the models. In the
case of deflections, it is noteworthy that in models 1 and 2, used by Whisenhunt (2004) and
Fisher (2005), the beam elements used to model intermediate diaphragms did not accurately
represent the flexural capabilities of these bridge components considering the lack of load
transferring evidenced on the deflected shape of these two models, that resemble the
deflected shape of a non skewed bridge, where there is little interaction between the girders
and the crossframes. Once these crossframes are modeled with two dimensional elements a
more suitable representation of the behavior is obtained. When comparing rotations on
models 3 and 4 to those obtained in the field, it can be seen that the use of gusset plates to
model the behavior of the end bent cross frames (model 4) enhanced the rotational response
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of the bridge dramatically, creating a more flexible structure that that on model 3. As far as
the deflections are concerned, both model 3 and 4 produced similar results to those obtained
from the field.
Figure 4-14. Deflections (top) and Transverse Rotations (bottom) for Roaring Fork
Bridge
-2.5
-2
-1.5
-1
-0.5
0
G1 G2 G3 G4 G5
DEF
LEC
TIO
N (
in)
GIRDER
DEFLECTIONS @ MIDSPAN
M1 M2 M3 M4 FIELD
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
G1 G2 G3 G4 G5
RO
TATI
ON
(d
eg)
GIRDER
WEB ROTATIONS @ MIDSPAN
M1 M2 M3 M4 FIELD
54
4.6 TIPS FOR MODELING
4.6.1 General
Following are a series of general modeling rules that were found to be helpful during the
Finite Element modeling stage of the investigation. The idea is to present a series of “useful
tips” to be accounted during the modeling process and to be considered only as guidelines for
future investigations. By no means should these tips be considered as mandatory.
4.6.2 Modeling Components
4.6.2.1 Girders and sole plates
It was observed from previous studies (Whisenhunt 2004 and Fisher 2005) that 8 noded
isoparametric shell elements are adequate to model steel girders and sole plates due to their
inherent ability to transfer shear forces as well as their membrane and bending capabilities.
Table 4-1 present the values for the geometrical dimensions of the girders and cross sections
of the bridges studied.
Table 4-1 Geometrical properties of the girders
b2
b1
t2
t1
tw
h
b1 (in) t1 (in) h (in) tw (in) b2 (in) t2 (in)
18.1 0.9 57.1 0.6 14.2 0.9
18.1 1.6 57.1 0.6 14.2 0.9
b1 (in) t1 (in) h (in) tw (in) b2 (in) t2 (in)
18 1 32 0.5 12 0.75
Chicken Road
Roaring Fork
55
It was found that an appropriate mesh size for the flanges was to divide the transverse
dimension (width) into units of at least one quarter of the bottom flange width, one half of the
top flange width and to divide the vertical dimension of the web into elements at least one
quarter of its height. Finally the span can be divided into units that can create an aspect ratio
of one or close to one. For the case of the two bridges studied this longitudinal dimension
was 3 inches for Roaring Fork Bridge and 100 mm (3.9 in) because this bridge was originally
detailed in metric units. Figure 4-15 presents an example of this situation.
This procedure not only ensures an adequate mesh density and keeps the element aspect ratio
as close to one as possible without severely affecting the computational time, but also
facilitates the SIP‟s coupling procedure by minimizing the eccentricity between the top
flange nodes and the SIP nodes.
The sole plates, on the other hand, were meshed using a criteria such that the nodes on the
part of the plate that was below the bottom flange would coincide as much as possible with
the nodes on the bottom flange above them. This means that the nodes on the plate would be
on the same vertical of the nodes on the bottom flange. By doing this, the process of creating
the rigid elements between them would be much easier.
Figure 4-15. Detail of the mesh on one of the girders of Roaring Fork Bridge
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4.6.2.2 Connectors and stiffeners
These particular components were modeled by creating a mesh of one half the top flange
element transverse dimension and the vertical size was adjusted to ease the coupling process
on the gusset plates on the end bent connectors as well as for the intermediate connectors,
depending on the type of crossframe used. However, the general idea was to locate the end
nodes of the crossframes / diaphragms coinciding as much as possible with the nodes on the
connectors to avoid unnecessary eccentricities between the coupled nodes. Figure 4-15 shows
the end bent stiffener meshed one half of the top flange element in the transverse dimension
of the girder and one half of the vertical dimension of the element.
4.6.2.3 Diaphragms
The end bent diaphragms were divided into as many elements on the diagonal direction as
the number of SIP end nodes converging into them. This number would depend upon the
geometry of the bridge, in particular upon the skew angle. The vertical size depended upon
the number of bolts connecting the gusset plates into the connectors. In this sense the criteria
use was to define as many vertical elements as bolts used. In that way the bolts location
would coincide with the mid nodes of the end elements, and the coupling process would be
facilitated. For the intermediate diaphragms the procedure was similar, but the size of the
elements along the axis of the diaphragm was one quarter of its total distance.
4.6.2.4 Stay In Place Forms (SIP’s), K-type and X-type intermediate crossframes.
The K and X type crossframes relative stiffness is considerably small compared to the much
larger girder. In consequence, it seems reasonable to model these structural components
using axially loaded truss elements that mimic a truss behavior, which basically means that
these elements are free to rotate at the connection on the stiffeners and their bending
capabilities will not be accounted for.
57
As for the case of the SIP forms, previous investigations from Helwig and Yura (2003) and
Whisenhunt (2004) demonstrated that the use of an X-brace truss system with two diagonals
produces a better representation of the shear stiffness of the SIP forms and also accounts for
the direction of in-plane shear transfer much more accurately. The procedures to determine
the SIP mechanical properties as well as the geometrical dimensions are also described by
Whisenhunt (2004).
Another interesting situation takes place at the end region of the SIP forms, where it was
required to use multi point constrain elements in order to link the ends of the SIP‟s with the
top strut or diaphragm of the end bent system. This was done to ensure proper behavior at
these regions although no SIP properties adjustment was required. A preliminary parametric
analysis proved that by refining the values of the mechanical properties of the SIP forms to
account for the change in length of the elements does not affect the behavior of the structure
more than 1%, suggesting it is not worth the effort.
4.6.2.5 Bearing Supports.
As it was mentioned on Section 4.4.3, Elastomeric Pads should be modeled with 20 noded
isoparametric solid elements since this higher order element can easily account for the typical
shear behavior of these components. Additionally it was found that in order to avoid
unnecessary and unreal stress concentrations at the end bents, it is required to model the
support by means of contact elements, which substantially reduce the amount of stress at that
region. Initial approaches only considered pinned nodes to constrain the interface between
the sole plate and the pad. However this condition induced great amount of “artificial”
stresses, which do not accurately model the behavior of that region. The difference between
the two approaches ranges around 15 to 20%.
58
In order to account for the eccentricity between the sole plate and the bottom flange, a grid of
rigid elements was assembled at the interface between the sole plate at the bearing and the
bottom flange. However, in none of the cases studied it was considered to eliminate the rigid
connectors and evaluate the response by simply linking both the bottom flange and the sole
plate directly. Hence it is not possible to compare the two choices but it is suggested that
future investigations take into consideration this condition.
4.6.2.6 End Bent Crossframes / Diaphragms
As it was mentioned before, at the end bent locations it was considered to not only
incorporate the gusset plates coupled to the end bent connectors but to include the typical
intermediate top gusset plate that links the diagonal members to the top strut. In general, this
intermediate plate is divided into eight elements arranged in a four by two configuration.
Preliminary analysis suggest that the size of this plate is not determinant in the rotational
behavior of the structure, and hence it can be inferred that it could be omitted, in which case
the diagonal elements could be directly attached to the intersection of the bottom flange and
the web of the channel at its mid span. Of course, further analysis must verify this
assumption. Figure 4-16 shows a detail of the end bent crossframes.
Figure 4-16. End Bent Detail of Chicken Road Bridge
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CHAPTER 5. A SIMPLIFIED MODEL PROCEDURE
5.1 Introduction
An extensive investigation was conducted herein in an effort to understand the lateral flange
bending phenomena that takes place in steel skewed bridges. Three different skew angles
were considered for the two bridges studied and the resulting data was statistically analyzed
in order to determine a possible trend that could potentially lead to identify the key
components required to propose a simplified model.
It turned out that the steel girders in skewed bridges showed a particular and peculiar
behavior, much different than those non skewed. In the end, it was possible to pinpoint key
elements such as the initial end and final end rotations, inflection points, and minimum and
maximum rotations.
With all the information gathered it was possible to develop a simplified model that consisted
of a function with upper and lower bounds which depended upon parameters such as
inflection point location, mid segment slope, and minimum and maximum values locations.
Following is a general description of the different steps that were taken in order to develop
the model.
It must be pointed out that besides the skew angle, results obtained on this section do not
account for changes on the response induced by variations in other parameters. This means
this simplified procedure was intended to provide an estimate of the transverse rotational
values for those bridges whose geometrical characteristics are similar the bridges used on this
investigation
60
5.2 Cross Section Rotations
As part of the investigation process to understand the torsional rotation behavior as well as to
determine the sensitivity of the system to the different parameters, rotations along the span
axis were selected to be the primary source of information. Although vertical deflections
were also considered, their effects have already been thoroughly studied by Whisenhunt
(2004) and Fisher (2005). The procedure used to determine rotations as well as sign
conventions in the investigation is shown in Figure 5-1.
Figure 5-1. Rotations on the girder cross section
The corresponding equations to determine top flange, web, and bottom flange rotations are
shown in Equations 5.1, 5.2 and 5.3
[Eq. 5-1]
x
y
TF
BF
X TF RIGHT
X TF MID
X TF LEFT
X BF RIGHT
X BF MID
X BF LEFT
Y
TF L
EFT
Y
TF M
ID
Y
TF R
IGH
T
Y
BF
RIG
HT
Y
BF
MID
Y
BF
LEFT
W
TF
W
BF
TF LEFT
TF MID
TF RIGHT
BF LEFT
BF MID
BF RIGHT
TF RIGHT TF LEFTTF
TF RIGHT TF LEFT
Y YTAN( )
X X TF
61
[Eq. 5-2]
[Eq. 5-3]
where all the variables shown can be determined using the notation defined on Figure 5-1.
5.3 Rigid Body Torsional Rotations
With the data obtained from the results of the finite element analysis it was possible to
determine that the variation between the top flange (TF) and bottom flange (BF) rotations
compared to the web (W) rotations were negligible. Even though the variations in the
rotational values were insignificant, the web rotations were always the highest among them
and therefore any conclusions derived from the use of web rotations will be conservative.
Knowing this fact, web rotations were selected as the representation of the overall cross
section. Figure 5-2 shows the rotations for one of the bridges at five different locations along
the span.
Figure 5-2. Rotations at 5 different locations for Roaring Fork Bridge
0.000
0.050
0.100
0.150
0.200
0.250
0.300
G1 G2 G3 G4 G5
RO
TATI
ON
S (D
EG)
INITIAL END BENT
TF
W
BF
0.000
0.050
0.100
0.150
0.200
0.250
0.300
G1 G2 G3 G4 G5
RO
TATI
ON
S (D
EG)
FIRST QUARTER
TF
W
BF
-0.200
-0.150
-0.100
-0.050
0.000
0.050
0.100
0.150
G1 G2 G3 G4 G5
RO
TATI
ON
S (D
EG)
MID SPAN
TF
W
BF
-0.300
-0.250
-0.200
-0.150
-0.100
-0.050
0.000
G1 G2 G3 G4 G5
RO
TATI
ON
S (D
EG)
THIRD QUARTER
TF
W
BF
-0.300
-0.250
-0.200
-0.150
-0.100
-0.050
0.000
G1 G2 G3 G4 G5
RO
TATI
ON
S (D
EG)
FINAL END BENT
TF
W
BF
BF MID TF MIDW
TF MID BF MID
X XTAN( )
Y Y W
BF RIGHT BF LEFTBF
BF RIGHT BF LEFT
Y YTAN( )
X X BF
62
5.4 The Rotations Profile
Throughout the investigation it was possible to single out several properties that seemed to be
inherent to the behavior of the steel skewed bridges. The torsional rotations profile was one
of them.
Typically girders in non skewed bridges experience rotations along their longitudinal axis
only in one direction (clockwise or counterclockwise). However, it was found that girders in
steel skewed bridges show a torsional rotation profile in which one part of the girder rotates
in one direction and the rest of the girder rotates in the opposite direction.
Figure 5-3. Rotations profile of an intermediate girder on Roaring Fork Bridge
-0.800
-0.600
-0.400
-0.200
0.000
0.200
0.400
0.600
0.800
0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00%
Ro
tati
on
(d
eg)
SPAN
Roaring Fork Rd Bridge - Girder #3
63
Figure 5-4. Rotations profile of an intermediate girder on Chicken Road Bridge
Figure 5-3 and Figure 5-4 show a typical rotation profile for an intermediate girder. When
comparing the average rotations profiles normalized with respect to the maximum absolute
value for both bridges it is possible to identify the similarities between them. Figure 5-5
shows this comparison. The evident similarities in shape support the idea of a systematic
behavior as far as torsional rotations are concerned.
Additionally, the rotations profile proved to be in good agreement with the field
measurements obtained. From this profile several key points were identified in order to
develop the simplified model to predict maximum and minimum rotations. This issue is
discussed in the next section.
-1.500
-1.000
-0.500
0.000
0.500
1.000
1.500
0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00%
Ro
tati
on
s (d
eg)
SPAN
Chicken Road Bridge -Girder #2
64
Figure 5-5. Comparison between normalized rotations in both bridges
Following there is a brief description of each of the key points that will be the major
components for the proposed simplified model.
5.4.1 Inflection point Location (X0)
Inflection points represent the location along the span of the girder where torsional rotations
are equal to zero. Throughout the investigation it was determined this value varies depending
upon the skew angle, as shown in Figure 5-6. After analyzing both the Chicken Road Bridge
and Roaring Fork Road Bridge data, it was possible to develop a general equation for the X0
value. X0 can be obtained using Eq. 5-4.
X0 = 66 – 0.35 x SKEW (deg) [Eq. 5-4]
This equation is valid for the mean value of X0 and for skew angles between 30 and 75
degrees. However, to establish a reasonable range, for Chicken Road Bridge a 15% variation
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00%
RO
TATI
ON
NO
RM
ALI
ZED
SPAN
45 DEG SKEW RF & 43 DEG SKEW CR (AVERAGE NORMALIZED)
RF CR
65
was found to be appropriate, whereas for Roaring Fork Road Bridge, a 10% variation led to
values within two standard deviations. Therefore,
Chicken Road: X0 -15% < Inflection Point Location < X0 +15%
Roaring Fork Road: X0 -10% < Inflection Point Location < X0 +10%
Figure 5-6. Variation of the inflection point location vs. skew angle for both bridges
5.4.2 The initial End rotations (i)
Although the ends of the bridge are laterally restrained by the End Bent cross-frames it was
found that rotations are developed at those locations. These rotations also vary depending
upon the skew angle of the bridge and the girder location (exterior or interior).
0
10
20
30
40
50
60
70
20 30 40 50 60 70 80
Span
(%
)
Skew Angle (deg)
Inflection Point Location
Xo CR
Xo RF
66
Figure 5-7. Initial rotations of Chicken Road Bridge (left) and Roaring Fork Bridge
(right)
Figure 5-7 depicts the values for the initial rotations of the first two girders of the two
bridges. It can be seen that the higher the skew the larger the difference between the
rotations. For Roaring Fork these differences were smaller than Chicken Road Bridge. In
addition, interior girders (G2) experienced higher rotations than the exteriors (G1).
5.4.3 The Final End rotations (f)
In the same fashion as the initial end rotations, the final end rotations also increase when the
bridge is more skewed. However, for this case the differences between exterior and interior
girders were negligible. Figure 5-8 depicts this situation.
Figure 5-8. Final rotations of Chicken Road Bridge (left) and Roaring Fork Bridge
(right)
-0.70
-0.60
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0 10 20 30 40 50 60 70 80R
ota
tio
n (
de
g)
Skew Angle (deg)
i
G1
G2
AVG
-0.70
-0.60
-0.50
-0.40
-0.30
-0.20
-0.10
0.00
0 10 20 30 40 50 60 70 80
Ro
tati
on
(d
eg)
Skew Angle (deg)
i
G1
G2
AVG
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 10 20 30 40 50 60 70 80
Ro
tati
on
s (d
eg)
Skew Angle (deg)
f
G1
G2
AVG
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 10 20 30 40 50 60 70 80
Ro
tati
on
(d
eg)
Skew Angle (deg)
f
G1
G2
AVG
i i
f f
i
67
5.4.4 Slopes- Overview
As part of the modeling process it was found that some of the possible parameters that allow
to simplify the analysis of the torsional rotations profile are the slopes of the straight portions
of the simplified model, which will be discussed later. However, for illustration purposes it is
worth mentioning that the model consists of three straight segments. The first segment begins
at the initial end rotation and finishes at the minimum rotation value. The middle segment
goes from the minimum rotation value, passes through the inflection point, and ends on the
maximum rotation location. The final segment starts at the maximum rotation location and
extends to the final end rotation. In any case, the slopes are valid for skew angles varying
from 30 degrees to 75 degrees. Following is a description of each slope considered on the
model.
5.4.4.1 Initial Segment Slope (mi)
Initial segment slope represents the slope of the straight line from the initial end rotation to
the minimum rotation along the span.
Figure 5-9 shows how this value changes as the skew angle is changed for both Chicken
Road Bridge (CR) and Roaring Fork Bridge (RF). As it was the case for the initial end
rotations, the slope values increase as we decrease the skew angle. However, for this
parameter the variation is almost linear.
It was determined that the data associated with this parameter yielded extremely high scatter,
and for that reason it will not be considered, at least initially, as a reliable source of
information for the model configuration.
68
Figure 5-9. Initial segment slope variation for both bridges
5.4.4.2 Middle Segment Slope (m0)
For the case of the middle slope the situation was clearly different. For this case the
maximum variation within the skew angles considered was about 15% for Chicken Road
Bridge and 10% for Roaring Fork Road Bridge, leading to upper and lower bound values of:
Chicken Road: m0 low = 0.85 m0 and m0 up = 1.15 m0
Roaring Fork Road: m0 low = 0.90 m0 and m0 up = 1.10 m0
It was proposed that for the general case, the middle segment slope mo can be estimated by:
m0 = 4.05 - 0.047 x SKEW (deg) [Eq. 5-5]
Figure 5-10 presents how the middle segment slope changes with skew angle.
-14
-12
-10
-8
-6
-4
-2
0
20 30 40 50 60 70 80
SLO
PE
(de
g)
SKEW ANGLE (deg)
mi
CR
RF
AVG
mi
69
Figure 5-10. Variation of the middle segment slope
5.4.4.3 Final Segment Slope (mf)
As it was found for the initial segment slope, the values for the final segment slope turned out
to be almost identical to the initial ones, as shown in Figure 5-11
Figure 5-11. Final segment slope variation
0.00
2.00
4.00
6.00
8.00
10.00
12.00
14.00
20 30 40 50 60 70 80
SLO
PE
(de
g)
SKEW ANGLE (deg)
mo
CR
RF
AVG
-14
-12
-10
-8
-6
-4
-2
0
20 30 40 50 60 70 80
SLA
OP
E (d
eg)
SKEW ANGLE (deg)
mf
CR
RF
AVG
m0
mf
70
Therefore, as it will be seen on the next section, when it comes to develop the simplified
model, they will be considered to have the same value. That is:
mi = mf [Eq. 5-6]
5.5 The proposed simplified model
After understanding the importance of each of the key components it was possible to come
up with a first approach to find a suitable way to easily model the transverse rotation
phenomenon. Figure 5-12 shows the proposed simplified model for the mean rotations
profile. It contains the different components that were found to have particular importance, as
mentioned before.
Figure 5-12. Proposed simplified model for mean values
xo
0% 100%
xmin
xmax
max
min
mo
m i
m f
SPAN (%)
RO
TATI
ON
(deg
)
i
f
71
It is worth mentioning that since the available data was limited only to two bridges it was
found to be appropriate to determine an upper and lower bound, in an effort to more
accurately represent the rotation profile.
It has to be pointed out that rotations are the combination of a number of independent factors
such as skew, geometric properties of the bridge, etc. Hence, it is likely their values are
normally distributed. This hypothesis could not be determined throughout the investigation
due to the limited data available. Nonetheless, it will be seen that assuming a confidence
interval of 95 % (two standard deviations to either side of the mean) the resultant intervals
strongly agreed with the data from the models. Figure 5-13 presents what this region looks
like.
Figure 5-13. Proposed region of results for the rotation profile
0% 100%
SPAN (%)
RO
TATI
ON
(deg
)
72
5.5.1 Minimum and Maximum Locations (Xmin, Xmax)
The locations for both the minimum and maximum rotation values can be determined by
using a geometric relationship between the initial segment of the model and the middle one.
An expression for Xmin can be developed as given by,
imin
i
m XX
m m
0 0
0
[Eq. 5-7]
where i is the initial end rotation in degrees, mo and mi are the middle segment and initial
segment slopes respectively in degrees, and X0 is the inflection point location in % of span.
Similarly, in order to determine the maximum rotation location, the resultant equation is,
0 0 f f
max
0 f
m X 100mX
m m
[Eq. 5-8]
where f is the final end rotation and mf is the final segment slope.
When the values of Xmin and Xmax are compared for the three skew angles, the resultant data is
shown on Figure 5-14 and Figure 5-15.
73
Figure 5-14. Distribution of locations of minimum rotations
Figure 5-15. Locations of maximum rotations with respect to the final end of the two
bridges
From the statistical analysis of this data it was found that a good approximation for the
location of the minimum and maximum rotation points is 20% from each end, as shown in
Table 5-1. However, due to the inherent scatter the upper and lower bounds can be found at
5% away from the median.
0.00
5.00
10.00
15.00
20.00
25.00
20 30 40 50 60 70 80
Span
(%
)
Skew Angle (deg)
Location of Minimum Rotation
Xmin CR
Xmin RF
0.00
5.00
10.00
15.00
20.00
25.00
20 30 40 50 60 70 80
Span
(%
)
Skew Angle (deg)
Location of Maximum Rotation
(100 - Xmax) CR
(100 - Xmax) RF
Xmin CR
Xmin RF
(100-Xmax ) CR
(100- Xmax ) RF
74
Table 5-1. Summary of minimum and maximum locations
5.5.2 Minimum and Maximum Values (min, max)
Once the key points were identified and its behavior understood it was possible to determine
both the location and values of the minimum and maximum rotations. The process by which
these values were determined is depicted in Figure 5-16.
Figure 5-16. Low and upper bound points for the minimum values
First the upper and lower bound values of the inflection point location (X0) are determined.
Using the expressions found for m0, Xmin using Eq. 5.5 and Eq. 5.7 respectively, and simply
following a geometrical analysis it is possible to solve for the lower minimum rotation, mean
minimum rotation, and upper minimum point rotations.
Skew (deg) Xmin CR (%) Xmin RF (%) (100 - Xmax) CR (%) (100 - Xmax) RF (%)
30 16.98 22.38 9.42 16.82
45 16.29 20.09 14.11 18.54
75 20.01 17.41 24.24 20.12
Average 17.76 19.96 15.92 18.49
Std Dev 1.98 2.48 7.57 1.65
Xmin Xmin upXmin low X0 X0 upX0 low
m0
m0 up
m0 low
min
min low
min up
SPAN
75
Three straight lines with slopes of m0 low, m0, and m0 up are drawn from each of the three
points, and intersected with those vertical from Xmin low, Xmin, and Xmin up to finally obtain min
low, min and min up.
Likewise, the maximum rotations can be found. For this case the three points are determined
by intersecting the three lines with slopes m0 low, m0, and m0 up with the vertical lines Xmax low,
Xmax, and Xmax up, as shown on Figure 5-17.
Figure 5-17. Lower and upper bound rotations for the maximum values
These numbers, in absolute value, are shown on Table 5-2 for different values of skew
between 30 and 75 degrees, which is the allowable range of values where the equations found
are deemed to be valid.
SPAN
Xmax Xmax upXmax lowX0 X0 upX0 low
max low
max
max up
m0
m0 up
m0 low
76
Table 5-2. Values and Location of minimum and maximum rotations
Generally speaking, what this procedure is aiming to do is to determine a region in which the
torsional rotations are expected to lie within. Additionally, linear interpolations are permitted.
Figure 5-18 portrays what this region looks like for one of the bridges.
Figure 5-18. Example of the lower and upper bounds on one of the bridges
SkewXmin
low
Xmin
Xmin
up
X0 low X0 X0 up
Xmax
low
Xmax
Xmax
up
min
low
min
min
up
max
low
max
max
up
(deg)
30.0 15 20 25 40.50 55.50 70.50 75 80 85 0.205 0.937 2.198 0.059 0.647 1.762
35.0 15 20 25 38.75 53.75 68.75 75 80 85 0.165 0.812 1.939 0.075 0.631 1.668
40.0 15 20 25 37.00 52.00 67.00 75 80 85 0.130 0.694 1.693 0.087 0.608 1.562
45.0 15 20 25 35.25 50.25 65.25 75 80 85 0.099 0.585 1.459 0.094 0.576 1.444
50.0 15 20 25 33.50 48.50 63.50 75 80 85 0.072 0.485 1.237 0.098 0.536 1.313
55.0 15 20 25 31.75 46.75 61.75 75 80 85 0.049 0.392 1.027 0.097 0.487 1.170
60.0 15 20 25 30.00 45.00 60.00 75 80 85 0.031 0.308 0.830 0.092 0.431 1.015
65.0 15 20 25 28.25 43.25 58.25 75 80 85 0.016 0.231 0.646 0.083 0.366 0.847
70.0 15 20 25 26.50 41.50 56.50 75 80 85 0.006 0.163 0.473 0.070 0.293 0.667
75.0 15 20 25 24.75 39.75 54.75 75 80 85 -0.001 0.104 0.313 0.053 0.211 0.474
(deg)(%) (%) (%) (deg)
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
0.80
0 20 40 60 80 100
RO
TATI
ON
S (d
eg)
SPAN (%)
Roaring Fork 45 deg
AVG + 2s
AVG
AVG - 2s
PROFILE
77
5.5.3 Example.
Let‟s consider a 60 degree skewed bridge. According to this procedure all that is needed to
do is to enter Table 5-3 with this skew angle and identify the corresponding minimum and
maximum mean rotations as well as the lower and upper bounds.
Table 5-3. Values for 60 deg skew
For this case, the minimum rotation is 0.031 deg for the lower bound, 0.308 deg for the
mean, and 0.83 deg for the upper bound. As far as the maximum rotations are concerned, the
lower bound is 0.092, the mean value is 0.431, and the upper bound is 1.015 deg.
SkewXmin
low
Xmin
Xmin
up
X0 low X0 X0 up
Xmax
low
Xmax
Xmax
up
m0
low
m0
m0
up
min
low
min
min
up
max
low
max
max
up
(deg)
55.0 15 20 25 31.75 46.75 61.75 75 80 85 0.73 1.47 2.20 0.049 0.392 1.027 0.097 0.487 1.170
60.0 15 20 25 30.00 45.00 60.00 75 80 85 0.62 1.23 1.85 0.031 0.308 0.830 0.092 0.431 1.015
65.0 15 20 25 28.25 43.25 58.25 75 80 85 0.50 1.00 1.49 0.016 0.231 0.646 0.083 0.366 0.847
(%) (%) (%) (deg) (deg) (deg)
78
5.6 Procedure to determine the Lateral Displacements (LD) on Steel skewed bridges
due to lateral flange bending.
Step 1. Compute the skew offset of the bridge.
If the bridge skew angle is smaller than 90 deg, then:
SKEW OFFSET (deg) = bridge skew angle (deg)
If the bridge skew angle is greater than 90 deg, then:
SKEW OFFSET (deg) = 180 deg - bridge skew angle (deg)
Step 2. Find the location of the inflection point (X0) and the slope of the middle portion (m0)
using Eq. 5-4 and Eq. 5-5:
X0 = 66 – 0.35 x SKEW OFFSET (deg)
m0 = 4.05 – 0.047 x SKEW OFFSET (deg)
Step 3. Determine the minimum and maximum rotations located at 20% of span and 80% of
span respectively. Use:
min = m0 (X0 – 20) / 100 or max = m0 (80 – X0) / 100
Step 4. Locate the Shear Center (S.C) of the girder cross section at 20% and 80% of span.
32 2
1 3 31 1 2 2
ht bh
t b t b
31 1
2 1 3 31 1 2 2
ht bh h h
t b t b
Figure 5-19. Girder X section
b2
b1
t2
t1
tw h2
h1
hN.A (x-x)
S.C
C.G
yN.A
79
Step 5. Find the maximum Lateral Displacements (LD), by computing:
LD max = max of 2 min
2 max
h x x / 180
h x x / 180
5.6.1 Example.
Let‟s consider the case of Chicken Road Bridge, with an average skew angle of 137 deg.
Step 1.
Since 137 deg > 90 deg, then: SKEW OFFSET (deg) = 180 -137 = 43 deg
Step 2.
X0 = 66 – 0.35 x 43 = 50.95 %
m0 = 4.05 – 0.047 x 43 = 2.029 deg
Step 3.
min = 2.029 (50.95 – 20) / 100 = 0.628 deg
max = 2.029 (80 – 50.95) / 100 = 0.589 deg
Step 4.
For Chicken Road Bridge:
b1 (in) t1 (in) h (in) tw (in) b2 (in) t2 (in)
18.11 0.87 57.1 0.63 14.17 0.87
80
Then:
3
1 3 3
57.1 0.87 14.17h 18.49 in
0.87 18.11 0.87 14.17
, h2 = 57.1 – 18.49 = 38.61 in
Step 5.
LD max = max of 2 min
2 max
h x x / 180
h x x / 180
=
38.61 x 0.628 x / 180 = 0.423 in
38.61 x 0.589 x / 180 = 0.399 in
LD max = 0.423 in
81
CHAPTER 6. PARAMETRIC ANALYSIS
6.1 Overview
This section discusses detailed information of the parametric study.
In order to determine relationships between different bridge parameters and the cross section
rotations a comprehensive parametric study was conducted. One of the most important
objectives was to determine the girders sensitivity to variations of one parameter at a time.
Due to the nature of the parameters considered on the investigation, it was considered
appropriate and convenient to divide them into two different categories. The first group will
include those parameters whose nature is such that they can be modified numerically. That is
the case of the “girder spacing to span ratio”, for example, on which the values of the
parameter change from one number to another. However, some of the parameters cannot be
varied in that fashion but non-numerically. A good example for this is the case of the
“crossframe type” parameter. It can be clearly seen this parameter can only be modified from
one crossframe type into another crossframe type ( i.e: from K- type to X-type, or vice
versa). Results from this parametric study are presented herein.
6.2 Numerical Parameters.
6.2.1 General
In an effort to determine the influence each parameter has on the bridge response a
comparison between them and the original values of each skew angle was carried out. This
was possible by determining the differential ratio between each case of study and its
corresponding original value. This is:
RATIO = [(case – original) / original] x 100 [Eq. 6-1]
82
where case represents the rotation value when a given parameter is under study and original is
the rotation value of the original case where no parameters were modified. After determining
which parameters induced important variations on the cross section rotations it was possible
to classify them in order of importance.
Parameters considered included exterior to interior moment of inertia (strong axis) ratio,
exterior to interior load ratio, number of girders, number of transverse stiffeners, number of
crossframes, crossframes stiffness, stay in place forms stiffness, and spacing to span ratio. In
each of the following plots in this section each case will be identified with the initials of the
bridge followed by the corresponding skew angle ( i.e. CR 43 stands for Chicken Road 43
deg skew).
Finally, a complete set of mitigation strategies was developed based upon a detailed
comparison of the different results obtained and the development of a classifying criteria for
the cases studied.
83
6.2.2 Exterior to Interior Moment of Inertia Ratio (Strong Axis)
During previous investigations carried out by Whisenhunt (2004) and Fisher (2005) one of
the most outstanding findings was the unusual deflection profile that steel skewed bridges
presented. This unexpected behavior had to do with the fact that exterior girders experienced
higher deflections than the interiors at a given section (Figure 6-1). Bearing that fact in mind
it was considered a possibility that changing the exterior to interior girders flexural stiffness
might have an important effect on the structure‟s behavior.
Figure 6-1. Typical cross section on the deflected shape at a given section along the span
For both Chicken Road Bridge and Roaring Fork Road Bridge four different skew angles
were considered. On Chicken Road 25, 43 (original), 75, and 90 degrees were considered
whereas for Roaring Fork Road 23 (original), 45,75, and 90 degrees were selected. For each
skew angle three different conditions were studied and rotations were monitored at both
flanges and the web.
The first condition included a 50% value for the parameter meaning the exterior girders
moment of inertia was half the value of the rest of the girders. This was possible by changing
the thicknesses for both the top and bottom flanges of the interior girders. The other cases
included the original value of 100% and the final case studied the effect when this parameter
is 200%.
Table 6-1 presents the rotation results.
DEFLECTED SHAPE
84
Table 6-1. Rotation values for the “Exterior to Interior Moment of Inertia” case
With the exception of the 75 degree skew angle for the 0.5X case on min and the 2.0X case
for max, all of the scenarios considered yielded good results. The change in the inertial
properties of the girders seems to have a beneficial effect on the rotations profile since most
of the resultant ratios were negative, meaning the rotations from each case were lower than
the original.
From Figure 6-2 and
Figure 6-3 it can be seen that the change in rotation values ranges between 20% and 40%.
However, in some cases the changes reach the value of 80%.
min CR 25 max CR 25 min RF 23 max RF 230.5X E-I INERTIA -11% -9% -31% -48%
ORIGINAL 0% 0% 0% 0%
2.0X E-I INERTIA -31% -27% -31% -17%
min CR 43 max CR 43 min RF 45 max RF 450.5X E-I INERTIA -15% -13% -24% -59%
ORIG 0% 0% 0% 0%
2.0X E-I INERTIA -43% -46% -42% 1%
min CR 75 max CR 75 min RF 75 max RF 750.5X E-I INERTIA -7% -16% 51% -80%
ORIGINAL 0% 0% 0% 0%
2.0X E-I INERTIA -52% -40% -77% 66%
CASESCR (25 DEG SKEW) RF (23 DEG SKEW)
RF (45 DEG SKEW)
RF (75 DEG SKEW)CR (75 DEG SKEW)
CR (43 DEG SKEW)CASES
CASES
85
Figure 6-2. Minimum rotations for the “Exterior to Interior Moment of Inertia” case
Figure 6-3. Maximum rotations for the “Exterior to Interior Moment of Inertia” case
-80%
-60%
-40%
-20%
0%
20%
40%
60%
80%
0.5X E-I INERTIA ORIG 2.0X E-I INERTIA
RA
TIO
CASES
min FOR "EXTERIOR TO INTERIOR MOMENT OF INERTIA"
CR 25 RF 23 CR 43
RF 45 CR 75 RF 75
-80%
-60%
-40%
-20%
0%
20%
40%
60%
80%
0.5X E-I INERTIA ORIG 2.0X E-I INERTIA
RA
TIO
CASES
max FOR "EXTERIOR TO INTERIOR MOMENT OF INERTIA"
CR 25 RF 23 CR 43
RF 45 CR 75 RF 75
86
6.2.3 Exterior to Interior Girder Load Ratio
Due to the difference in tributary load between exterior and interior girders it is reasonable to
expect unequal rotational behavior of the exterior and interior girders.
A total of twenty four finite element models were generated to investigate how exterior to
interior girder load ratio affects steel girder rotations. For Chicken Road Bridge three
different values were selected for this parameter: 50%, 85% (original), and 100%. Four
different skews were included: 25, 43 (original), 75, and 90 degrees. As for the case of
Roaring Fork Bridge, values of 50%, 67% (original), and 100% were considered along with
skew angles of 23 (original), 45, 75, and 90 degrees.
Table 6-2 presents results for this analysis.
Table 6-2. Rotation values for the “Exterior to Interior Girder Load Ratio” case
min CR 25 max CR 25 min RF 23 max RF 23E-I LOAD 50% -25% -20% -14% -3%
ORIGINAL 0% 0% 0% 0%
E-I LOAD 100% 13% 10% 19% 2%
min CR 43 max CR 43 min RF 45 max RF 45E-I LOAD 50% -23% -14% -16% 4%
ORIGINAL 0% 0% 0% 0%
E-I LOAD 100% 10% 7% 29% -8%
min CR 75 max CR 75 min RF 75 max RF 75E-I LOAD 50% -28% -8% -56% 17%
ORIGINAL 0% 0% 0% 0%
E-I LOAD 100% 12% 4% 106% -31%
CASESCR (75 DEG SKEW) RF (75 DEG SKEW)
CASESCR (25 DEG SKEW) RF (23 DEG SKEW)
CASESCR (43 DEG SKEW) RF (45 DEG SKEW)
87
For the case of the exterior to interior load parameter, results leave no doubt that increasing
this number is not favorable in terms of the torsional effect it produces (see Figure 6-4 and
Figure 6-5). A physical explanation relies upon the fact that an increase in this number
represents a structure with wider overhangs, and all the forces transmitted to the exterior
girders close to the bottom flanges via the falsework brackets generate undesirable horizontal
forces that lead to twisting moments on the cross section. Consequently, a higher tendency to
rotate along the longitudinal axis occurs. Let‟s recall that a factor of 100% on this parameter
represents an overhang width equal to one half the girders spacing, whereas a 50% factor
means no overhang whatsoever.
Figure 6-4. Minimum rotations distribution for the “Exterior to Interior Load Ratio”
case
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
120%
E-I LOAD 50% ORIG E-I LOAD 100%
RA
TIO
CASES
min FOR "EXTERIOR TO INTERIOR LOAD RATIO"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
88
Figure 6-5. Maximum rotations distribution for the “Exterior to Interior Load Ratio”
case
-60%
-40%
-20%
0%
20%
40%
60%
80%
100%
120%
E-I LOAD 50% ORIG E-I LOAD 100%
RA
TIO
CASES
max FOR "EXTERIOR TO INTERIOR LOAD RATIO"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
89
6.2.4 Number of Girders
During Fisher„s (2005) investigation it was found that the effect the number of girders has on
the overall behavior of the steel skewed bridges was negligible. Nevertheless, it was worth
reconsidering the potential sensitivity the structure has to rotations of the cross section.
Four different values were selected for both Chicken Road and Roaring Fork Bridges.
Calling “N” the number of girders, N-1, N (Original), N+2, and N+5 models were
considered. For each value three skews were studied leading to a total of twenty four
different finite element models studied. The skew angles involved were 30, 45, and 75
degrees. Results are presented on Table 6-3.
Table 6-3. Rotation values for the “Number of Girders” case
min CR 25 max CR 25 min RF 23 max RF 23N-1 -3% 10% -1% -2%
ORIGINAL 0% 0% 0% 0%
N+2 -7% -18% -4% -5%
N+5 -20% -35% -5% -8%
min CR 43 max CR 43 min RF 45 max RF 45N-1 -2% 0% -5% -3%
ORIGINAL 0% 0% 0% 0%
N+2 3% 0% 3% 3%
N+5 3% 3% 7% 3%
min CR 75 max CR 75 min RF 75 max RF 75N-1 -1% -4% -3% -5%
ORIGINAL 0% 0% 0% 0%
N+2 -1% 5% -7% 6%
N+5 -2% 9% 4% 3%
CASESCR (75 DEG SKEW) RF (75 DEG SKEW)
CASESCR (25 DEG SKEW) RF (23 DEG SKEW)
CASESCR (43 DEG SKEW) RF (45 DEG SKEW)
90
Figure 6-6 and Figure 6-7 present the ratios of transverse rotational change for the cases
studied. Results obtained for this parameter suggest that as the number of girders is increased
the torsional rotations tend to increase, leading to positive ratios. However, this is not the
case for low values of skew, of which the behavior is just the opposite.
In any case when the average change was computed for all of the cases studied the overall
result was a change that ranged between ±5%. This results confirm what Fisher (2005) found
for deflections.
Figure 6-6. Minimum rotations distribution for the “Number of Girders” case
-40%
-30%
-20%
-10%
0%
10%
20%
N-1 ORIG N+2 N+5
RA
TIO
CASES
min FOR "# OF GIRDERS"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
91
Figure 6-7. Maximum rotations distribution for the “Number of Girders” case
Figure 6-8 presents the bridge model for the case in which the number of girders is 10.
Figure 6-8. Roaring Fork Bridge with N+5 Girders (10 Girders)
-40%
-30%
-20%
-10%
0%
10%
20%
N-1 ORIG N+2 N+5
RA
TIO
CASES
max FOR "# OF GIRDERS"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
1
X
Y
Z
92
6.2.5 Number of Transverse Stiffeners
Two of the main reasons why transverse stiffeners are used on steel girders is to control out
of plane deformations at a given location and to prevent web buckling or crippling, etc. The
possibility of modifying the torsional stiffness at discrete locations led to considering this
parameter in the investigation.
Three values were analyzed for this parameter. However, the values were selected based
upon the number of original intermediate stiffeners for each girder and increasing them by a
given factor. For the case of Chicken Road, its original six stiffeners per side on the interior
girders were modified by a factor of 11/6 and 14/6 while for Roaring Fork these factors were
5/3 and 7/3 because Roaring fork has three stiffeners per side of interior girder. Table 6-4
shows the results for this study.
Table 6-4. Rotation values for the “Number of Transverse Stiffeners” case
min CR 25 max CR 25 min RF 23 max RF 23ORIGINAL 0% 0% 0% 0%
1.67X # STIFFENERS -26% -30% -4% -4%
2.33X # STIFFENERS -5% 9% -35% -14%
min CR 43 max CR 43 min RF 45 max RF 45ORIGINAL 0% 0% 0% 0%
1.67X # STIFFENERS -11% -3% -1% -2%
2.33X # STIFFENERS -1% -12% -3% -5%
min CR 75 max CR 75 min RF 75 max RF 75ORIGINAL 0% 0% 0% 0%
1.67X # STIFFENERS -16% -17% 0% -2%
2.33X # STIFFENERS -12% -13% -2% -5%
CASESCR (75 DEG SKEW) RF (75 DEG SKEW)
CASESCR (25 DEG SKEW) RF (23 DEG SKEW)
CASESCR (43 DEG SKEW) RF (45 DEG SKEW)
93
Similar to what happened with the Exterior to Interior Moment of Inertia Ratio, the addition
of stiffeners along the span of the girders proves to be effective as far as torsional rotations is
concerned, evidenced on Figure 6-9 and Figure 6-10. The results suggest that enhancing the
torsional stiffness of the girders yields important changes in the cross section rotational
behavior, at least up to 20%. The values range between 5% and 25%, reaching a one time the
value of 30%.
Figure 6-9. Minimum rotations distribution for the “Number of Transverse Stiffeners”
case
-40%
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
ORIG 1.67X # STIFFENERS 2.33X # STIFFENERS
RA
TIO
CASES
min FOR "NUMBER OF TRANSVERSE STIFFENERS"
CR 25 RF 23 CR 43
RF 45 CR 75 RF 75
94
Figure 6-10. Maximum rotations distribution for the “Number of Transverse
Stiffeners” case
Figure 6-11 presents an image of the additional transverse stiffeners along the span of the
girder. Notice that for this case there is an extra transverse stiffener between intermediate and
end bent crossframes.
Figure 6-11. Detail of the stiffeners distribution for the 2.33X case on Chicken Road
Bridge
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
ORIG 1.67X # STIFFENERS 2.33X # STIFFENERSR
ATI
O
CASES
max FOR "NUMBER OF TRANSVERSE STIFFENERS"
CR 25 RF 23 CR 43
RF 45 CR 75 RF 75
1
95
6.2.6 Number of Crossframes
In an effort to determine how sensitive steel skewed bridges are to the number of crossframes
or diaphragms a series of analyses were carried out.
For the two bridges three values for this parameter were considered. They ranged from a
structure with no crossframes (#XF 0X) to a structure with twice the number of crossframes
(#XF 2.0X). Again, as it has been done with the rest of the parameters, three skew angles
were considered for each bridge. Table 6-5 presents the results of the study on this parameter
Table 6-5. Rotation values for the “Number of Crossframes” case
min CR 25 max CR 25 min RF 23 max RF 23# XF 0X -93% -92% -98% -98%
ORIGINAL 0% 0% 0% 0%
# XF 2X -48% -48% -20% -37%
min CR 43 max CR 43 min RF 45 max RF 45# XF 0X -86% -88% -93% -94%
ORIG 0% 0% 0% 0%
# XF 2X -47% -49% 0% -22%
min CR 75 max CR 75 min RF 75 max RF 75# XF 0X -58% -58% -69% -86%
ORIG 0% 0% 0% 0%
# XF 2X -43% -38% 23% -21%
CASESCR (75 DEG SKEW) RF (75 DEG SKEW)
CASESCR (25 DEG SKEW) RF (23 DEG SKEW)
CASESCR (43 DEG SKEW) RF (45 DEG SKEW)
96
From the data obtained there are several observations. The fact that the best results were
obtained when no crossframes are provided may support the idea that the major cause of
torsional rotations are the presence of crossframes along the bridge, either staggered or not.
The fact that forces and stresses can be distributed along the girders via the crossframes leads
to the theory that rotations are the consequence of an inherent behavior of the steel skewed
bridges, and rotations will always be part of their behavior (See Figure 6-12 and Figure
6-13).
Figure 6-12. Rotations distribution for the “Number of Crossframes” case
-100%
-80%
-60%
-40%
-20%
0%
20%
40%
# XF 0X ORIG # XF 2X
RA
TIO
CASES
min FOR "NUMBER OF CROSS FRAMES"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
97
Figure 6-13. Maximum rotations distribution for the “Number of Crossframes” case
Nevertheless, when the crossframes are doubled the effect is interesting. The overall ability
of the girders to rotate against the longitudinal axis is enhanced up to 30% on average, with
values varying from 0% to almost 50%. Figure 6-14 presents Roaring Fork Bridge with twice
the number of crossframes for a 75 degree skew angle case.
Figure 6-14. Roaring Fork Bridge at 75 deg skew with twice the original number of
Crossframes
-100%
-80%
-60%
-40%
-20%
0%
20%
40%
# XF 0X ORIG # XF 2X
RA
TIO
CASES
max FOR "NUMBER OF CROSS FRAMES"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
1
X
Y
Z
98
6.2.7 Crossframe Stiffness
Another parameter considered in the analysis was the crossframe stiffness. For Chicken Road
Bridge this parameter was directly associated with the crossframe members cross section
area, due to the fact that in a K-type or X-type crossframe the overall stiffness is provided by
the axial rigidity of each member. For Roaring Fork Road Bridge the situation is different
since diaphragms provide both axial and flexural stiffness. Therefore both the cross sectional
area and the moment of inertia of the strong axis were evaluated.
For Chicken Road a total of three different stiffnesses, including the original, were
considered. The cross section areas of the members were modified to half of the original and
twice the original. For Roaring Fork Road Bridge it was necessary to evaluate both the
moment of inertia along the strong axis and cross section area independently since the
diaphragms provide both flexural and axial rigidity to the system. Both the moment of inertia
and the cross section area were modified independently to half and twice the original for the
three different skew angles studied. Results obtained are presented on Table 6-6.
Table 6-6. Rotation values for the “Crossframe Stiffness” case
min CR 25 max CR 25 min RF 23 max RF 23 min RF AX 23 max RF AX 230.5X INERTIA X-F 0% 0% -5% -9% -5% 0%
ORIGINAL 0% 0% 0% 0% 0% 0%
2.0X INERTIA X-F 0% 0% -3% 5% -1% -4%
min CR 43 max CR 43 min RF 45 max RF 45 min RF AX 45 max RF AX 45
0.5X INERTIA X-F 0% 0% -1% 1% -4% -7%
ORIGINAL 0% 0% 0% 0% 0% 0%
2.0X INERTIA X-F 0% 0% 3% 0% 7% 5%
min CR 75 max CR 75 min RF 75 max RF 75 min RF AX 75 max RF AX 75
0.5X INERTIA X-F 0% 0% -7% 5% 5% -9%
ORIGINAL 0% 0% 0% 0% 0% 0%
2.0X INERTIA X-F 0% 0% 28% -8% 12% 6%
FLEX STIFFNESS AXIAL STIFFNESS
CASESCR (25 DEG SKEW) RF (23 DEG SKEW) RF (23 DEG SKEW)
CASES
CASES
CR (43 DEG SKEW) RF (45 DEG SKEW)
CR (75 DEG SKEW) RF (75 DEG SKEW)
RF (45 DEG SKEW)
RF (75 DEG SKEW)
99
Contrary to what could be thought, changes in the crossframe stiffness do not show a unique
trend. The idea that stiffer crossframes could be beneficial to the structure is not necessary
the case.
Figure 6-15 and Figure 6-16 demonstrate that modifying either the axial or the flexural
stiffness does not provide the desired response when the crossframes system is composed of
diaphragms. There are cases in which these changes produce a less stiff structure, evidenced
by the increase in rotational values. Based upon the data obtained it seems that it is better to
enhance the flexural stiffness of a diaphragm by increasing its moment of inertia rather than
its cross section area. Changes in the stiffness of the K-type crossframes did not show
significant variations.
Figure 6-15. Minimum rotations distribution for the “Crossframes Stiffness” case
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
0.5X INERTIA X-F ORIG 2.0X INERTIA X-F
RA
TIO
CASES
min FOR "CROSS FRAMES STIFFNESS"
CR 25 RF 23 RF AX 23
CR 43 RF 45 RF AX 45
CR 75 RF 75 RF AX 75
100
Figure 6-16. Maximum rotations distribution for the “Crossframes Stiffness” case
-10%
-5%
0%
5%
10%
15%
20%
25%
30%
0.5X INERTIA X-F ORIG 2.0X INERTIA X-F
RA
TIO
CASES
max FOR "CROSS FRAMES STIFFNESS"
CR 25 RF 23 RF AX 23
CR 43 RF 45 RF AX 45
CR 75 RF 75 RF AX 75
101
6.2.8 Stay in Place Forms Stiffness
Although not included in current design codes, it has been demonstrated that the stay in place
metal deck forms provide some lateral stiffness to the structure before the composite
behavior of the bridge slab. (Jetann et al, 2002; Egilmez et al, 2003 and 2006). Considering
this, it makes sense to modify the stay in place form stiffness to determine how these changes
affect the overall behavior of the bridge.
To investigate this parameter for each of the two bridges and the three skew angles in the
study, three different stay in place form stiffnesses were considered, including the original.
Table 6-7 summarizes these cases mentioned.
Table 6-7. Rotation values for the “Stay in Place Forms Stiffness” case
min CR 25 max CR 25 min RF 23 max RF 23SIP 0.1X 37% 11% 18% 23%
ORIGINAL 0% 0% 0% 0%
SIP 10X -13% -21% -17% -10%
min CR 43 max CR 43 min RF 45 max RF 45SIP 0.1X 12% 6% 3% 9%
ORIGINAL 0% 0% 0% 0%
SIP 10X -1% -2% -2% -4%
min CR 75 max CR 75 min RF 75 max RF 75SIP 0.1X -2% 6% -24% 17%
ORIGINAL 0% 0% 0% 0%
SIP 10X 4% -4% 22% -11%
CASESCR (75 DEG SKEW) RF (75 DEG SKEW)
CASESCR (25 DEG SKEW) RF (23 DEG SKEW)
CASESCR (43 DEG SKEW) RF (45 DEG SKEW)
102
Results from the study of this parameter are presented on Figure 6-17 and Figure 6-18. These
results present a clear trend in which the higher the cross section area of the SIP elements the
lower the rotations on the structure. These values reach up to 10% to 15% average for skew
angles lower than 75 degrees. This is clear evidence that even though the SIP forms provide
some lateral bracing especially during the construction phase, a small improvement on the
connection system, which is usually the weakest part of the system, would be beneficial for
the entire structure.
These results are in good agreement with those obtained by Egilmez et al. (2007). They
suggested that by enhancing the connection details between the SIP forms and the girders,
which is the weakest point of this structural component, it is possible to improve the strength,
stiffness and overall performance of the system.
Figure 6-17. Minimum rotations distribution for the “Stay In Place Forms Stiffness”
case
-30%
-20%
-10%
0%
10%
20%
30%
40%
SIP 0.1X ORIG SIP 10X
RA
TIO
CASES
min FOR "STAY IN PLACE FORMS STIFFNESS"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
103
Figure 6-18. Maximum rotations distribution for the “Stay In Place Forms Stiffness”
case
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
25%
SIP 0.1X ORIG SIP 10X
RA
TIO
CASES
max FOR "STAY IN PLACE FORMS STIFFNESS"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
104
6.2.9 Girder Spacing to Span Ratio
Previous investigations regarding differential deflections carried out by Wisenhunt (2004)
and Fisher (2005) came to the conclusion that this particular parameter has an important role
on the deflection values. Likewise, it was considered worth checking whether this condition
is also applicable to torsional transverse rotations.
Four different spacing to span ratio values were studied for the two bridges, which are 0.5
times the original, the original, 1.25 times the original, and two times the original. However,
due to the geometric constraints associated with each bridge cases with a skew angle lower
than 30 degrees could not have values determined. Table 6-8 presents the results for all the
above cases.
Table 6-8 Rotation values for the “Girder Spacing to Span Ratio” case
min CR 25 max CR 25 min RF 23 max RF 23SPC-SPN 0.5X 30% 68% 11% 17%
ORIGINAL 0% 0% 0% 0%
SPC-SPN 1.25X 11% -24% -12% -35%
min CR 43 max CR 43 min RF 45 max RF 45SPC-SPN 0.5X 3% 0% 6% -10%
ORIGINAL 0% 0% 0% 0%
SPC-SPN 1.25X -1% -2% 0% 1%
SPC-SPN 2X -15% -33% -5% -9%
min CR 75 max CR 75 min RF 75 max RF 75SPC-SPN 0.5X 3% -7% 7% -31%
ORIGINAL 0% 0% 0% 0%
SPC-SPN 1.25X -2% 1% 1% 5%
SPC-SPN 2X -6% 4% 5% 0%
CASESCR (75 DEG SKEW) RF (75 DEG SKEW)
CASESCR (25 DEG SKEW) RF (23 DEG SKEW)
CASESCR (43 DEG SKEW) RF (45 DEG SKEW)
105
From Figure 6-19 and Figure 6-20 it can be noticed that the worst scenario occurs when this
parameter is changed to values lower than one. However, when those values are increased
above one there seems to be a slight decrease in the rotations values, particularly for skew
angles lower than 75 degrees. Although the change is within 15% to 20% of average, it
represents an alternative to be considered for controlling torsional rotations of the structure.
Although it may sound logical to modify the amount of dead load on the structure when the
spacing to span ratio is modified, this was not the case since the main objective was to
evaluate changes in the response for one variable at a time. Nevertheless results suggest that
when this parameter is set less than one, the stiffness of the intermediate diaphragms is
increased and therefore their capacity to transfer forces from one girder to its adjacent
promoting transverse deformations along the span. Conversely, when the value of this
parameter is set greater than one, the diaphragms become more slender and therefore more
flexible, decreasing their ability to transfer lateral loads. Figure 6-21 presents a picture of one
of the bridges when this parameter is set to 0.5.
Figure 6-19. Minimum rotations distribution for the “Spacing to Span Ratio” case
-40%
-20%
0%
20%
40%
60%
80%
SPC-SPN 0.5X ORIG SPC-SPN 1.25X SPC-SPN 2X
RA
TIO
CASES
min FOR "SPACE TO SPAN RATIO"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
106
Figure 6-20. Maximum rotations distribution for the “Spacing to Span Ratio” case
Figure 6-21. Roaring Fork Bridge with a 75 deg skew and a Space / Span Ratio half of
the original
-40%
-20%
0%
20%
40%
60%
80%
SPC-SPN 0.5X ORIG SPC-SPN 1.25X SPC-SPN 2X
RA
TIO
CASES
max FOR "SPACE TO SPAN RATIO"
CR 25 RF 23
CR 43 RF 45
CR 75 RF 75
1
X
Y
Z
107
6.2.10 Analysis of Results
From the parametric analysis it can be determined, among other things, how sensitive the
structure is to changes of a particular variable. Some of the parameters demonstrated to be
less effective and some proved to be of vital importance in the final rotational response of the
steel girders.
In an effort to provide a better understanding of the torsional rotations effects of each
variable the parameters were classified in order of effectiveness in modifying the response.
The criteria utilized to classify the parameters was based on a tolerance margin set to plus
minus 5%; where those situations that led to changes higher than 5% were considered to be
unfavorable and those that fell under -5% were defined as favorable. Regardless of the values
selected as boundaries, perhaps the most important outcome was related to the idea of
establishing possible mitigation strategies and criteria oriented towards controlling the
torsional rotations phenomenon. The proposed classification is as follows:
6.2.10.1 Favorable Parameters (Ratio > 5%)
This expressions corresponds to those parameters that, when modified, yield a torsionally
stiffer structure. This is a structure whose torsional rotations are lower than those on the
original.
6.2.10.1.1 Increase either the exterior girders or the interior girders moments of
inertia
The best effects were obtained by changing the values of this parameter. On average,
by increasing the internal girders moment of inertia the rotations were decreased by
20%, whereas by increasing the exterior girders moment of inertia the change
produced a reduction of 28% of the torsional rotations.
108
6.2.10.1.2 Increase the number of crossframes
After modifying this variable by a factor of 2 the average rotation reductions was
around 28%, which is similar than what the previous condition generated.
6.2.10.1.3 Increase the Number of Transverse Stiffeners
This condition, on average, was capable of reducing the rotations up to 10% for the
three skew angles and on both bridges.
6.2.10.2 Neutral Parameters (-5% ≤ Ratio ≤ 5%)
This classification was intended to cover those cases in which changes in the corresponding
parameters did not produce, on average, significant changes in the girder response, either
positive or negative. These cases are:
6.2.10.2.1 Modify the number of girders
Although it may be reasonable to think that the larger the number of girders the
smaller the maximum rotations, this does not seem to be true. This is based on the
idea that as we increase the number of girders, the “local” effect of both the skewness
and the unbalanced tributary load should fade off. However results do not agree with
this theory. In fact, for the three values considered (N-1, N+2 and N+5) the highest
or lowest average change for any case was 3%.
6.2.10.2.2 Modify the stiffness of the crossframes
Another condition somewhat unexpected was that increasing or decreasing the
crossframe stiffness by factors of 2 and ½ respectively, did not produce substantial
changes on the rotation values. In any case, the results demonstrated that the
maximum absolute change was 2%.
109
6.2.10.2.3 Increase the stiffness of the SIPs
By increasing this variable by a factor of 10 the average change in rotation values was
only 2%, which means that as long as this parameter is not modified, there will not be
any undesirable effects as it is the case when the value of this parameter is reduce,
that will be discussed in the following section.
6.2.10.3 Unfavorable Parameters (Ratio < -5%)
When the value of one parameter is modified such that it yields increments of the transverse
rotation, then it is defined as an unfavorable parameter. Following there is a list of those that
satisfy this condition.
6.2.10.3.1 Increase in the exterior to interior load ratio
When this parameter was changed to the extreme amount of 100%, the original idea
was to monitor the effect of increasing the sizes of overhangs on the structure as well
as to verify how effective this condition is in modifying the average torsional
rotations of the girders. It turns out that the worst change that can be done to a bridge,
as far as torsional rotations are concerned, is this condition. The average increase in
rotations for all the skews and bridges studied was 14%.
6.2.10.3.2 Decrease in the stiffness of the Stay in Place metal deck forms
It was mentioned before that increasing the SIPs stiffness by a factor of 10 did not
produce major changes on the rotational values. However, when this condition is
inversed the outcome is not the same. Indeed, decreasing the SIPs stiffness by a factor
of 10 causes the rotations to increase by 10%.
110
6.2.10.4 Summary of Numerical Cases
After analyzing all the different results obtained from the parametric study it was possible to
identify potential sources for mitigation strategies. For example, if for a given bridge
potential torsional rotation problems are identified then one possible solution would be to
increase the torsional stiffness of the girders by increasing the moment of inertia of the
exterior ones. Figure 6-22 depicts the average rotation ratios for all the parameters considered
in this investigation. It can be noted that some cases lie within the neutral zone (ie. N+2),
whereas others fall outside, either on the unfavorable area above +5% (ie. SIP 0.1X) or on
the favorable area below -5% (ie. #XF 2X).
Although some of the values adopted for the parameters are not technically reasonable, their
study suggests a possible trend on the results that is necessary to understand the degree of
influence a parameter has on the girder response.
Figure 6-22. Results from the study on numerical parameters
-35%
-30%
-25%
-20%
-15%
-10%
-5%
0%
5%
10%
15%
20%
Ro
tati
on
al R
atio
Parameters
Summary of Parametric Results
Neutral
Favorable
Unfavorable
111
6.3 Non-numerical Parameters
6.3.1 Crossframe Layout.
6.3.1.1 Overview
A preliminary parametric analysis was conducted in order to determine the influence of the
crossframe layout on the overall behavior of the structure. Three different layouts were
considered on this investigation, which include the original staggered case, the case where
crossframes are perpendicular to the girder web and aligned with each other and finally the
case where crossframes are laid out parallel to the abutments and aligned to one another.
Figure 6-23 presents these three layouts.
Figure 6-23. Layouts considered: Staggered (left), Parallel (center) and Perpendicular
(right)
Additionally, each layout was evaluated for three different skew angles on each of the two
bridges included along the investigation. These skew angles were 25, 43 and 75 deg for
Chicken Rd. Bridge and 23, 45 and 75 deg for Roaring Fork. Bridge. The results were
compared for both the transverse rotations and longitudinal stresses and the most interesting
findings are presented.
6.3.1.2 Comparison of Results
The initial analysis consisted of determining both maximum rotations and average stresses
along the structure for the each of the three skew angles selected. For each case the values
were compared in an effort to identify possible trends that might lead to useful conclusions.
112
Figure 6-24 presents the distribution of the maximum average transverse rotations for both
Chicken Rd. Bridge and Roaring Fork. Bridge. It can be seen that the staggered option is the
one that shows the highest rotational values for most of the cases included. This is also
evidenced when comparing the average maximum stresses on the girders.
In this sense Figure 6-25 presents the average maximum stresses measured along the girders.
It is possible to notice that the staggered alternative provides the highest average stresses for
almost the entire data. This result strongly agrees with the rotation results evidencing the fact
that perhaps the staggered scenario is not the most adequate for this type of steel bridges.
Figure 6-24. Rotations on Chicken Rd. (left) and Roaring Fk. Rd (right) Bridges
Figure 6-25. Average maximum stresses on Chicken Rd. (left) and Roaring Fork Rd.
(right) Bridges
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 10 20 30 40 50 60 70 80
RO
TATI
ON
S (d
eg)
SKEW ANGLE(deg)
MAX AVERAGE ROTATIONS ON CHICKEN RD BRIDGE
STAG
PERP
PARAL
0.00
0.20
0.40
0.60
0.80
1.00
1.20
0 10 20 30 40 50 60 70 80
RO
TATI
ON
S (d
eg)
SKEW ANGLE(deg)
MAX AVERAGE ROTATIONS ON ROARING FK BRIDGE
STAG
PERP
PARAL
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
0 10 20 30 40 50 60 70 80
F /
Fy (
%)
SKEW ANGLE (deg)
MAX AVERAGE STRESS RATIOS ON CHICKEN RD BRIDGE
STAG
PERP
PARAL
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
0 10 20 30 40 50 60 70 80
F /
Fy (
%)
SKEW ANGLE (deg)
MAX AVERAGE STRESS RATIOS ON ROARING FK BRIDGE
STAG
PERP
PARAL
113
Nonetheless, in an effort to have a broader picture of the situation, another parameter was
considered in the analysis. Figure 6-26 presents the total crossframe forces for each scenario.
In this Figure each point represents the summation of all the total forces on each crossframe
located between the corresponding girders. It can be observed that the staggered alternative is
not the best option for two of the three skew angles studied on Chicken Road Bridge.
However, the case on Roaring Fork Bridge is somewhat different. This is due to the fact that
the diaphragm system has not only the possibility of transferring forces from one girder to
the other as it is the case of the crossframes but its flexural stiffness also contributes to the
force flow between adjacent girders by its capability of transferring moments. Results show
that while perpendicular layout produced the highest forces on all cases the parallel
configurations produced the lowest. For all the cases studied, as the skew angle moves
towards 90 degrees the forces are smaller, indicating less interaction between girders and
crossframes.
(a) (d)
(b) (e)
0
50
100
150
200
250
300
350
G1-G2 G2-G3 G3-G4
Forc
e (K
ip)
Forces on Cross Frames (25 deg. Skew) on Chicken Rd.
25 stagg
25 perp
25 paral
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
G1-G2 G2-G3 G3-G4 G4-G5
Forc
e (k
ip)
Total Cross Frame Forces on Roaring Fk. (23 deg Skew)
Staggered
Perpend
Parallel
0
50
100
150
200
250
300
350
G1-G2 G2-G3 G3-G4
Forc
e (K
ip)
Forces on Cross Frames (43 deg. Skew) on Chicken Rd.
43 stagg
43 perp
43 paral
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
G1-G2 G2-G3 G3-G4 G4-G5
Forc
e (k
ip)
Total Cross Frame Forces on Roaring Fk. (45 deg Skew)
Staggered
Perpend
Parallel
114
(c) (f)
Figure 6-26. Total Crossframe forces for the three skew angles studied.
(a) CR 25 (b) CR 43 (c) CR 75 (d) RF 23 (e) RF 45 (f) RF 75
The situation regarding the 75 degrees configuration is also particular. It can be seen from
Figure 6-27 that the three layouts are so similar and so close to each other that it could be
anticipated that any of the options would give the best results. This is expected to be the case
as the skew angle approaches to 90 degrees.
Figure 6-27. Plan view of the three crossframe layouts overlapped for 75 degree skew
on Chicken Rd. Bridge
0
50
100
150
200
250
300
350
G1-G2 G2-G3 G3-G4
Forc
e (K
ip)
Forces on Cross Frames (75 deg. Skew) on Chicken Rd.
75 stagg
75 perp
75 paral
0.0
5.0
10.0
15.0
20.0
25.0
30.0
35.0
40.0
45.0
50.0
G1-G2 G2-G3 G3-G4 G4-G5
Forc
e (k
ip)
Total Cross Frame Forces on Roaring Fk. (75 deg Skew)
Staggered
Perpend
Parallel
Staggered Perpendicular Parallel
115
6.3.2 Crossframe Type (X-Type vs. K-Type)
6.3.2.1 General
A parametric analysis was conducted to determine the influence of the type of crossframe in
the overall response of the bridge. Two types of crossframe configurations were included (K-
type and X-type) and three different skew angles (25, 43 and 75 deg.) were selected to
determine the sensitivity of the system to these parameters. Additionally, for both types of
crossframes, the same cross section was selected (L 3 ½ x 3 ½ x ½). In order to study the
response, cross section rotations were selected as the comparison criteria. It is worth
mentioning that the analysis was carried only for Chicken Road Bridge, because it was the
only bridge that was designed with one of these crossframe geometries.
6.3.2.2 Preliminary Analysis
In order to have an initial idea of how the system behaves with each of the crossframe
configurations selected, a preliminary study was conducted by subjecting each configuration
to a unit load in both the horizontal and vertical directions, as it is shown on Figure 6-28.
Whisenhunt (2004) carried out a similar analysis but only considering vertical deflection. He
found that both systems yielded relatively similar results.
Figure 6-28. Crossframe and unit load configurations
Rigid Element
Rigid Element
Unit Load
Angles
Angle
Angles
Angle
Rigid Element
Rigid Element
Unit Load
Angles
Angle
Rigid Element
Rigid Element
Unit Load
Angles
Angle
Rigid Element
Rigid Element
Unit Load
(a) (b)
(c) (d)
116
Each truss system was composed of diagonals and struts with the actual angle cross section,
whereas the vertical elements that correspond to the girders cross sections were considered to
be much stiffer than the angles. Although the assumptions related to the top strut as well as
the girders cross section are not entirely true, the main purpose was to perform a relative
analysis, on which both truss systems are subjected to the same load and boundary
conditions.
After performing the analysis it was found that both systems yielded almost the same vertical
deflections for cases (b) and (d) on Figure 6-28. However, when the lateral deformations
were studied, which corresponds to cases (a) and (c) on Figure 6-28, the outcome was much
different. It turns out that the X-type system yielded lateral deformations 50% smaller than
the K-type.
Having this in mind it is possible to expect higher rotations on the K-type system, but same
vertical deflections on both, as it was mentioned by Whisenhunt (2004).
6.3.2.3 Comparison of Results
Figure 6-29 presents what was found to be the distribution of maximum rotations with
respect to the skew angle.
It can be clearly seen that, as expected, the X-type of crossframe yielded much lower values
of rotations than the K-type. However as we approach a non skewed bridge (90 degrees), the
difference tends to reduce. This agrees with the fact that transverse rotations for a non
skewed bridge are negligible when compared to the skewed configuration.
117
Figure 6-29. Distribution of transverse rotations versus skew angle on Chicken Road
Bridge
As a general recommendation, it seems reasonable to select X-type crossframes for those
bridges with severe skew angles in order to have a more efficient control of the rotations.
0.000
0.200
0.400
0.600
0.800
1.000
1.200
1.400
0 10 20 30 40 50 60 70 80 90
RO
TATI
ON
(d
eg)
SKEW ANGLE (deg)
EFFECT OF CROSS FRAME TYPE ON CHICKEN RD BRIDGE
K-type
X-type
118
6.3.3 Dead Load Fit
6.3.3.1 Overview
Some of the topics related to differential deflections on steel skewed bridges have been
addressed in several documents. In particular AASHTO/NSBA (2003) accounts for this
condition by stating, among other things, that designers should indicate the condition under
which diaphragms fit (no-load fit, full dead load fit or any condition in between). When
designers consider full dead load, they must anticipate the transverse rotations if girders need
to be plumb, however AASHTO/NSBA (2003) admits that the rotations are only a prediction
and therefore at the final stage of the loading process the girders may end up being somewhat
out-of-plumb. It can be inferred from the aforementioned statement that the current
knowledge on the rotational response of steel skewed bridges is not sufficient to provide
more accurate guidelines.
In an effort to address these issues a parametric analysis was implemented. A description of
the procedure adopted as well as results and observations are presented herein.
6.3.3.2 General Procedure.
In order to determine the influence of the dead load fit condition on the bridge behavior, a
general but simple procedure was implemented. In essence, the main objective was to
compare the responses for both the transverse rotations and the longitudinal stresses on the
following cases:
When dead loads were applied to the original straight structure.
When dead loads were applied to the cambered structure.
To achieve this objective, the following methodology was adopted to model the cambered
structure. First, it was required to compute the deformations on the initially straight girders in
all of the three directions (x, y and z). Once these deformations were obtained, they were
119
subtracted from the nodal coordinates of the original straight structure to create the nodal
coordinates on the cambered structure. Although this methodology may sound quite simple,
it proved to be very effective. Equation 6-2 presents this calculation.
cambered straight straight i i i [Eq. 6-2]
where represents either the x, y or z coordinate and i is the node number.
Figure 6-30 and Figure 6-31 present a cross section of a girder at four different stages, and
for simplicity only one node was identified. For the straight girder case the initial condition,
labeled as State A, and the final stage, labeled as State B are presented on Figure 6-30. For
the selected node (TF right) both the transverse and the vertical deflections were identified as
XTF RIGHT STR and YTF RIGHT STR respectively. On the other hand, Figure 6-31 shows the
same situation but for the cambered case. In this condition, State C represents the initial
situation whereas State D accounts for the final one, with the correspondent transverse and
vertical deformations, identified as XTF RIGHT CAMB and YTF RIGHT CAMB respectively.
Figure 6-30. Initial (State A) and final (State B) conditions of a cross section on a
straight skewed bridge.
TF RIGHT
x
y
X TF RIGHT STR
Y TF RIGHT STR
W
STATE A STATE B
120
Figure 6-31. Initial (State C) and final (State D) conditions of a cross section on a
cambered skewed bridge
Part of the investigation was focused on determining whether or not the deflections and
stresses that take place on the straight case are similar to the ones obtained on the cambered
model. Perhaps the most important reason for this has to do with the typical asymmetry of
both the plan view and the cross section view of a skewed bridge. Hence, predictions on the
response were not easy and it was required to perform a sensitivity study that could help us in
clarifying this issue.
In order to have a better picture of the potential influence of designing the girders specifying
a full dead load fit, a parametric analysis was carried out on which the skew angle of one of
the bridges was selected as the variable. In this sense, three different skew angles were
selected, including the original angle, and the rotational and stress responses were normalized
with respect to the non skewed case.
6.3.3.3 Analysis of Results
Figure 6-32 and Figure 6-33 present what it was found to be the typical stress response
obtained when comparing the straight and the cambered cases. In both figures the plotted
TF RIGHT
X TF RIGHT CAMB
Y TF RIGHT CAMBW
STATE C STATE D
x
y
121
data represent the stress distribution of the difference between two cases in study for an
exterior girder.
Figure 6-32. Distribution of the difference in stresses on an exterior girder between the
cambered and the straight models at the top flange on a 23 deg. skew angle bridge
Figure 6-33. Distribution of the difference in stresses on an exterior girder between the
cambered and the straight models at the bottom flange on a 23 deg. skew angle bridge.
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT Cross Frames
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT Cross Frames
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
122
It can be seen that both behaviors look very similar, in particular along the stable region, as
will be defined on Chapter 7. In fact, it was found that the maximum stress difference at this
region was within ±5% for the three skew angles selected on the parametric analysis. In the
case of rotations the situation is quite similar. Figure 6-34 and Figure 6-35 depict this
condition for two contiguous girders. The dashed line represents the normalized difference
obtained from the two cases. As in the stresses distributions, the maximum difference
observed was within ±5%.
Figure 6-34. Distribution of normalized rotations and their difference for an exterior
girder on a 23 degree skew angle
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1
23 DEGREES CAMBERED
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
123
Figure 6-35. Distribution of normalized rotations and their difference for an interior
girder on a 23 degree skew angle.
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2
23 DEGREES CAMBERED
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
124
6.3.4 Pouring Sequence
6.3.4.1 Overview
The issues related to the pouring sequence on steel bridges have been the subject of study in
several investigations. The National Cooperative Highway Research Program (NCHRP)
(2005) has accounted for this condition through a publication that presented the results of a
survey study on the steel bridge erection practices nationwide. Some of the interesting
concerns that arose from that study had to do with the pouring sequence practices. As a
result, in an effort to address those concerns a parametric analysis was carried out on which
the skew angle was selected as the main parameter. The objective was to determine whether
or not adopting a different pouring sequence could affect the response of the structures as far
as rotations and longitudinal stresses are concerned.
In this sense, the pouring sequence adopted in the investigation only considered the case
when the central half of the slab is cast. The reason lays in the fact that it is not only common
practice particularly in continuous span steel bridges but also it is highly expectable that
rotations and stresses induced by this condition will be close to those obtained from the full
dead load. The study incorporated three different skew angles (23, 45 and 75 degrees) and
the non skewed case (90 degrees) for normalization purposes transverse torsional rotations as
well as longitudinal stresses were considered as the comparison parameters.
6.3.4.2 Analysis of Results
As it was the case on the Dead Load Fit analysis carried out on section 6.3.3, the normalized
rotations and the longitudinal stresses were compared to the correspondent original full load
case. By doing this it was possible to have an idea of how sensitive the structure is to changes
in the loading scenarios, in this case addressed by the pouring sequence. Figure 6-36 and
Figure 6-37 present what was found to be the stress profiles for an exterior girder at both the
top and bottom flanges.
125
Figure 6-36. Distribution of the difference in LFB stresses on an exterior girder between
the pouring sequence adopted and the original model at the top flange on a 45 deg. skew
angle bridge.
Figure 6-37. Distribution of the difference in LFB stresses on an exterior girder between
the pouring sequence adopted and the original model at the bottom flange on a 45 deg.
skew angle bridge.
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
126
From both previous figures it is apparent that with the exception of the peak values at the
cross frame locations, the difference in stresses is very low. In fact, the maximum stress
difference along the stable region was found to be within a ±5% for all the three different
skew angles considered. This particular behavior highlights the idea that the magnitude of the
longitudinal stresses that take place within the girders when concrete is cast on the middle
section of the bridge are in the same order of magnitude than those obtained by casting the
whole structure. Figure 6-38 shows what it was found to be the average percent reduction in
both deflections and rotations when using the proposed pouring sequence. It can be seen that
while deflection reduction seems to be constant around 25%, rotations reductions tend to be
sensitive upon the skew angle. In fact, as the skew angle approaches to 90 the average
percent reduction seems to be less. However, we must bear in mind that absolute rotations
values for a non skewed bridge are insignificant, as it was shown before.
Figure 6-38. Comparison between average percent reduction in deflections and
rotations with respect to the original pouring sequence
0
5
10
15
20
25
30
0 20 40 60 80 100
% R
ed
uct
ion
Skew Angle (deg)
Average Percent Reduction
ROTATION DEFLECTION
127
Although no composite effect was considered throughout this investigation, it is expected
that once the middle strip of concrete is poured approximately 75% of the total dead load
deflections and rotations (for skew angles between 30 and 75 degrees) will be locked in once
the concrete hardens. This means that by adopting this proposed pouring sequence significant
improvements will be achieved in controlling rotations and deflections resulting from casting
the remainder of the slab and therefore it is less likely that the bridge might experience
excessive deformations that could lead to other potential problems.
Figure 6-39 and Figure 6-40 show what was found to be the distribution of normalized
rotations along the span for an exterior and interior girder respectively, including the
difference between them (dashed line). As it was expected, along the stable zone (see
Chapter 7) the difference obtained is almost zero. This, along with the stress distribution
already covered, demonstrates that a great deal of the total transverse rotations take place by
loading the central zone of the bridge.
Figure 6-39. Distribution of normalized rotations and their difference for an exterior
girder on a 45 degree skew angle
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 45 DEGREE SKEW ANGLE
45 DEGREES 50% LOAD
45 DEGREES ORIGINAL
45 DEGREES DIFFERENCE
128
Figure 6-40. Distribution of normalized rotations and their difference for an interior
girder on a 45 degree skew angle.
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 45 DEGREE SKEW ANGLE
45 DEGREES 50% LOAD
45 DEGREES ORIGINAL
45 DEGREES DIFFERENCE
129
CHAPTER 7. LATERAL FLANGE BENDING STRESSES
7.1 General
Current design codes related to structures in the transportation field, such as the AASHTO
Guidelines for Design for Constructability (2003), have stated that designers are required to
consider the possible effects that differential deflections may have on a bridge structure.
Particularly, design codes are concerned with the unexpected issues that might arise due to
the lateral flange bending phenomenon typical of skewed bridges with staggered crossframes.
A comprehensive study was conducted to verify and quantify the overall flexural stresses that
take place in the flanges under this condition.
In Chapter 5 it was stated that it seems reasonable to consider the cross section torsional
rotation as a rigid body rotation and therefore consider web rotations as the representation of
the overall torsional behavior of the girder. With this assumption it was possible to
determine the stress profile due to Lateral flange bending (LFB) for both the top and bottom
flanges. It was found that in no case did these stresses exceed 10% of the corresponding yield
strength, and that the shape of the stress profile was particularly affected by the stress
concentrations occurring at the vicinity of the crossframes and supports.
7.2 Sources of Stress Concentration
Throughout the investigation, and particularly during the finite 3D element modeling phase,
it was possible to determine that at some locations along the structure the presence of stress
concentrations due to either geometric or structural constraints could be noticeable. These
locations were identified as the primary sources of variation of the stress results profile that
could ultimately lead to erroneous conclusions if not handled properly. Hence, it was
required to characterize these modeling anomalies inherent to the process and make sure they
were accurately described during the analysis stage.
130
7.2.1 Stress concentrations at the End Bents.
The end bents of the girders consisted of a series of shell elements that defined each
component of the bridge at this location. These components are the girder flanges and web,
the end bent stiffener (or connector), the sole plates, the elastomeric pad, the gusset plates,
and the diaphragm.
Particular attention must be given to the end connector, which must not carry the load
transmitted by the diaphragm but also transfer the typically high forces from the supports
across the cross section of the girder.
Figure 7-1 shows how the stresses flow in the vicinity of the supports. It can be noticed that
besides the gusset plates that link the diaphragms to the girders, the highest stress
concentrations are located towards the ends of the top and bottom flanges and spread along
the span. This was later evidenced in the erratic behavior of the stress profile at the end bent
surroundings.
Figure 7-1. Longitudinal stress contours at the end bents.
1
JUN 14 2009
22:35:03
Stress concentrationand area of influence
End BentDiaphragm
Top Flange
Web
Gusset Plate
131
7.2.2 Stress concentrations at the Intermediate Crossframes or Diaphragms
The intermediate crossframes not only have the function of providing adequate lateral
bracing to the structure, but also guarantee enough redundancy to distribute forces and
stresses all over the bridge. Hence, it is expected that high stress concentrations will develop
at their connections within the superstructure considering they are discretely distributed
along the span of the girders. In other words, the flow of forces and moments that are
developed continuously along the span of the girder has only a discrete number of locations
to get transferred from one girder to the other, leading to an important force flow density at
the vicinity of the intermediate connectors. Figure 7-2 depicts this situation. Although the
contours do not show a stress variation as important as they were on the end bents, the
localized effect of the connectors spreads along the span.
7.2.3 Other possible sources
Although the previous two conditions seemed to be the most determinant on the stress
profile, other possible sources, such as the stay in place forms, were observed. However, this
particular component did not prove to be crucial in any of the cases included in the analysis
and their effect was considered negligible.
Figure 7-2. Stress concentrations along the span on top and bottom flanges
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12:46:01
Stress concentrationand area of influence
Intermediate Diaphragm
132
7.3 The LFB stress profile
One of the things we must bear in mind when studying the lateral flange bending stress
problem is the need to isolate the lateral stress component from the total stresses acting on
both the bottom and the top flanges. This means that it is required to identify the two sources
of longitudinal stresses that take part in the analysis. From solid mechanics, the total
longitudinal stresses that act on a beam subjected to multiaxial loading come from both the
web flexure and from the lateral flange flexure.
Figure 7-3 shows a decomposition of the two different stresses acting on the flanges. First the
flexural stress coming from the action of moments perpendicular to the plane of the web
(Mweb) and last, but not least, stresses due to moments perpendicular to the plane of the
flanges (Mflange). In order to determine the stresses due to Mflange (LFB), solid mechanics tells
us the following:
LFB TOTAL WEB
[Eq. 7-1]
where TOTAL is the total stress at the point and WEB is the stress due to Mweb.
With this relationship it is possible to determine the actual stress that is caused by the LFB
condition.
133
Figure 7-3. Combined Longitudinal stresses on a girder section
Figure 7-4 and Figure 7-5 present what is found to be the typical total stress distribution
along the span for an external girder and the corresponding LFB stress profile. It can be
noticed the recurrent presence of disturbances evidenced in the peak values for both the top
and bottom flanges. For the bottom flange, disturbances were more drastic at the end bents.
WEB BENDING(due to Mweb)
LATERAL FLANGEBENDING(due to Mflange)
TOTAL STRESSES
Mweb
Mflange
Mflange
Mweb
z x
y
COMBINED FLEXURAL STRESSES
134
Figure 7-4. Total stress distribution on top flange of an exterior girder
Figure 7-5. Total stress distribution on bottom flange of an exterior girder
When this analysis is carried out on an interior girder, the situation is different. The existence
of crossframes on both sides of the girder has a major influence on the stress response. See
Figure 7-6 and Figure 7-7.
-40
-30
-20
-10
0
10
20
0 10 20 30 40 50 60 70 80 90 100
STR
ESS
(ksi
)
SPAN (%)
TOTAL LONGITUDINAL STRESSES ON TOP FLANGE OF G1
TOP LEFT TOP MID TOP RIGHT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-40
-30
-20
-10
0
10
20
0 10 20 30 40 50 60 70 80 90 100
STR
ESS
(ksi
)
SPAN (%)
TOTAL LONGITUDINAL STRESSES ON BOT. FLANGE OF G1
BOTTOM LEFT BOTTOM MID BOTTOM RIGHT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
135
Figure 7-6. Total stress distribution on top flange of an interior girder
Figure 7-7. Total stress distribution on bottom flange of an interior girder
-40
-30
-20
-10
0
10
20
0 10 20 30 40 50 60 70 80 90 100
STR
ESS
(ksi
)
SPAN (%)
TOTAL LONGITUDINAL STRESSES ON TOP FLANGE OF G2
TOP LEFT TOP MID TOP RIGHT
TOPLEFT
TOPRIGHT
TOPMID
G1G3
-40
-30
-20
-10
0
10
20
0 10 20 30 40 50 60 70 80 90 100
STR
ESS
(ksi
)
SPAN (%)
TOTAL LONGITUDINAL STRESSES ON BOT. FLANGE OF G2
BOTTOM LEFT BOTTOM MID BOTTOM RIGHT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
G1G3
136
When the WEB element is “filtered” from the total, it is then possible to visualize the LFB
component.
In order to normalize the results related to LFB stresses the ratios of LFB stress versus Fy
were also monitored, which aid to determine whether the stresses would lie within certain
values. The location of the crossframes along the span was included in order to compare
them with the peak values on the stress profile, as it is shown on Figure 7-8 and Figure 7-9
for the exterior girders.
Figure 7-10 and Figure 7-11, on the other hand, show what is found to be the general profile
for the LFB stresses on an interior girder for both bridges.
Figure 7-8. Normalized LFB stress profile for on the top flange of an exterior girder
-40
-30
-20
-10
0
10
20
30
0 10 20 30 40 50 60 70 80 90 100
F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT Cross Frames
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
137
Figure 7-9. Normalized LFB stress profile for on the bottom flange of an exterior girder
Figure 7-10. Normalized LFB stress profile for on the top flange of an interior girder
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOT. FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT Cross Frames
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
-40
-30
-20
-10
0
10
20
30
0 10 20 30 40 50 60 70 80 90 100
F/Fy
(%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT Crossframes
TOPLEFT
TOPRIGHT
TOPMID
G1G3
138
Figure 7-11. Normalized LFB stress profile for on the bottom flange of an interior
girder
7.4 LFB stress profile characteristics
From the stress profiles obtained during the investigation it was possible to identify some of
the key characteristics of its behavior.
7.4.1 Key Regions
Figure 7-12 shows the two different regions that can be pinpointed. It can be clearly noted a
region, typically on the central part of the span in which stresses tend to be less disturbed.
This “stable” zone range varies depending on whether we consider the bottom or top flange.
Results also show this value is sensitive to the location of the girder in the structure, whether
it is an exterior or an interior girder. Table 7-1 presents the values found for this stable range
along the span in percent.
-30
-20
-10
0
10
20
30
0 10 20 30 40 50 60 70 80 90 100F/Fy
(%)
SPAN (%)
LATERAL BENDING STRESSES ON BOT. FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT Crossframes
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
G1G3
139
Figure 7-12. Key regions on a typical LFB stress profile
The case of the disturbed regions shows stress peaks that tend to be higher the closer we get
to the supports. This condition evidences the unstable behavior developed close to the
supports where stress concentrations seem to be critical. Evidently, the stress values in this
region were disregarded as far as the conclusions were concerned, since the accumulation of
stress concentration places distort the actual values.
It is worth mentioning that the parameters considered for this analysis were limited to one
favorable (Chapter 6), one neutral, and one unfavorable case in an effort to evaluate the
correspondence between the mitigation criteria based upon the rotation profile and the LFB
stress profile.
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL FLANGE BENDING STRESS PROFILE
Cross Frames BOTTOM LEFT BOTTOM RIGHT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
STABLE ZONE
PEAKS AT THE CROSSFRAME
LOCATIONS
DISTURBED REGIONS
140
Table 7-1. Bounds for the stable region.
7.4.2 “Locked-in” Stresses due to LFB
As mentioned previously, once the LFB stress profile is determined it is possible to identify
the magnitude of these stresses within the stable region. This is particularly important when
the time comes to establish the most efficient and adequate mitigation strategy.
It was observed that regardless of the bridge considered there is no indication of a possible
trend to determine the locations of these maximum and minimum stress points within the
stable region. In some cases they are close to the midspan but in other cases they are towards
the ends of the stable zone. However, as far as the stress values are concerned, they proved to
be higher on the bottom flange. Table 7-2 and Table 7-3 present a summary of the maximum
and minimum stresses due to LFB within the stable zone. The values are presented in percent
from the yield stress (F/Fy) and the location on the span is also presented as LOC (%). It can
be observed that the values lie below 18%.
MIN (%) MAX (%) MIN (%) MAX (%)
Chicken Road 43 deg Skew G1 25 82 17 88
Chicken Road 43 deg Skew G2 14 87 16 79
Chicken Road E-I LOAD 100% (43 deg) G1 20 77 17 88
Chicken Road E-I LOAD 100% (43 deg) G2 20 80 16 79
Chicken Road E-I INERTIA 2X (43 deg) G1 20 81 18 88
Chicken Road E-I INERTIA 2X (43 deg) G2 21 87 15 84
Roaring Fork 23 deg Skew G1 13 63 23 87
Roaring Fork 23 deg Skew G2 7 96 33 70
Roaring Fork 23 deg Skew G3 5 97 34 64
Roaring Fork E-I LOAD 100% (23 deg) G1 14 66 23 87
Roaring Fork E-I LOAD 100% (23 deg) G2 6 96 15 86
Roaring Fork E-I LOAD 100% (23 deg) G3 6 96 14 86
Roaring Fork E-I INERTIA 2X (23 deg) G1 9 47 23 86
Roaring Fork E-I INERTIA 2X (23 deg) G2 6 97 44 70
Roaring Fork E-I INERTIA 2X (23 deg) G3 6 96 34 66
BOTTOM FLANGE TOP FLANGEBRIDGE PARAMETER GIRDER
141
Table 7-2. Summary of Stresses on the Bottom Flange
Table 7-3. Summary of Stresses on the Top Flange
LOC (%) VALUE (%) LOC (%) VALUE (%)
Chicken Road 43 deg Skew G1 20 -4 80 4
Chicken Road 43 deg Skew G2 70 -9 71 8
Chicken Road E-I LOAD 100% (43 deg) G1 20 -5 78 5
Chicken Road E-I LOAD 100% (43 deg) G2 70 -6 71 5
Chicken Road E-I INERTIA 2X (43 deg) G1 20 -2 20 3
Chicken Road E-I INERTIA 2X (43 deg) G2 46 -6 46 5
Roaring Fork 23 deg Skew G1 27 0 28 4
Roaring Fork 23 deg Skew G2 41 -11 40 11
Roaring Fork 23 deg Skew G3 40 -8 58 7
Roaring Fork E-I LOAD 100% (23 deg) G1 15 -2 31 2
Roaring Fork E-I LOAD 100% (23 deg) G2 92 -5 7 6
Roaring Fork E-I LOAD 100% (23 deg) G3 92 -6 92 6
Roaring Fork E-I INERTIA 2X (23 deg) G1 25 -4 23 4
Roaring Fork E-I INERTIA 2X (23 deg) G2 41 -18 41 16
Roaring Fork E-I INERTIA 2X (23 deg) G3 40 -18 0 15
HIGH STRESSBRIDGE PARAMETER GIRDER
BOTTOM FLANGELOW STRESS
LOC (%) VALUE (%) LOC (%) VALUE (%)
Chicken Road 43 deg Skew G1 34 -3 34 5
Chicken Road 43 deg Skew G2 24 -2 24 5
Chicken Road E-I LOAD 100% (43 deg) G1 33 -2 33 5
Chicken Road E-I LOAD 100% (43 deg) G2 24 -3 24 6
Chicken Road E-I INERTIA 2X (43 deg) G1 36 -4 36 4
Chicken Road E-I INERTIA 2X (43 deg) G2 26 -4 26 5
Roaring Fork 23 deg Skew G1 20 -5 21 7
Roaring Fork 23 deg Skew G2 24 -8 24 8
Roaring Fork 23 deg Skew G3 47 -3 49 3
Roaring Fork E-I LOAD 100% (23 deg) G1 41 -2 40 3
Roaring Fork E-I LOAD 100% (23 deg) G2 21 -6 21 6
Roaring Fork E-I LOAD 100% (23 deg) G3 27 -6 27 7
Roaring Fork E-I INERTIA 2X (23 deg) G1 62 -5 61 7
Roaring Fork E-I INERTIA 2X (23 deg) G2 51 -5 50 6
Roaring Fork E-I INERTIA 2X (23 deg) G3 60 -4 39 4
BRIDGE PARAMETER GIRDER LOW STRESS HIGH STRESS
TOP FLANGE
142
7.5 LFB stress profile analysis
7.5.1 LFB vs. Torsional displacements
One of the questions that arise once the LFB stress profile is known is what determines its
behavior. Is it due to the rotational phenomena or not? In order to answer this question the
stress profiles were compared to both the LFB rotational and displacement profiles.
In Chapter 5 it was demonstrated that rigid body motion controls the rotational behavior of
the cross section of the girders particularly in those regions away from the crossframe
connections. Knowing that fact, comparisons were carried out between the total lateral
displacement, the lateral displacements due to torsional rotations, and the lateral
displacements due to LFB. The reason to do this was to determine what component of the
total displacement is the one that agrees with the stress profile.
Figure 7-13 presents one of these comparisons. It reflects the typical behavior for all of the
cases studied. Hence, from this comparison it is clearly stated that it is the torsional behavior
that seems to control the lateral displacements of the girders of steel skewed bridges.
Figure 7-13. Bottom flange (left) and Top flange (right) displacements
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
-15
-10
-5
0
5
10
15
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
DIS
PLA
CEM
ENT
(in
)
DIS
PLA
CEM
ENT
(mm
)
SPAN (%)
DISPLACEMENT COMPONENTS ON BOTTOM FLANGE
TOTAL ST. VENANT'S LFB
-0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
-15
-10
-5
0
5
10
15
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
DIS
PLA
CEM
ENTS
(in
)
DIS
PLA
CEM
ENTS
(m
m)
SPAN (%)
DISPLACEMENT COMPONENTS ON TOP FLANGE
TOTAL ST. VENANT'S
143
Table 7-4 and Table 7-5 present a summary of the peak displacements from the total lateral
displacements for both the bottom and top flanges. Likewise, Table 7-6 shows the peak
displacements obtained from the LFB displacements profile.
Table 7-4. Summary of Lateral Displacements on the Bottom Flange
Table 7-5. Summary of Lateral Displacements on the Top Flange
LOC (%) LOC (%)
Chicken Road 43 deg Skew G1 88 -0.63 in 17 0.47 in
Chicken Road 43 deg Skew G2 90 -0.54 in 9 0.50 in
Chicken Road E-I LOAD 100% (43 deg) G1 17 -0.54 in 88 0.65 in
Chicken Road E-I LOAD 100% (43 deg) G2 10 -0.55 in 91 0.57 in
Chicken Road E-I INERTIA 2X (43 deg) G1 16 -0.21 in 87 0.31 in
Chicken Road E-I INERTIA 2X (43 deg) G2 10 -0.27 in 89 0.24 in
Roaring Fork 23 deg Skew G1 29 -0.10 in 82 0.30 in
Roaring Fork 23 deg Skew G2 18 -0.20 in 81 0.20 in
Roaring Fork 23 deg Skew G3 18 -0.20 in 83 0.20 in
Roaring Fork E-I LOAD 100% (23 deg) G1 15 -0.03 in 79 0.20 in
Roaring Fork E-I LOAD 100% (23 deg) G2 61 -0.04 in 40 0.07 in
Roaring Fork E-I LOAD 100% (23 deg) G3 61 -0.04 in 40 0.07 in
Roaring Fork E-I INERTIA 2X (23 deg) G1 14 -0.01 in 74 0.20 in
Roaring Fork E-I INERTIA 2X (23 deg) G2 18 -0.02 in 46 0.20 in
Roaring Fork E-I INERTIA 2X (23 deg) G3 61 -0.05 in 40 0.08 in
TOTAL DISPLECEMENTS BOTTOM FLANGE
VALUE VALUE
MIN DISPLACEMENT MAX DISPLACEMENTBRIDGE PARAMETER GIRDER
LOC (%) LOC (%)
Chicken Road 43 deg Skew G1 94 -0.52 in 14 0.47 in
Chicken Road 43 deg Skew G2 91 -0.54 in 8 0.49 in
Chicken Road E-I LOAD 100% (43 deg) G1 95 -0.50 in 15 0.57 in
Chicken Road E-I LOAD 100% (43 deg) G2 94 -0.52 in 14 0.55 in
Chicken Road E-I INERTIA 2X (43 deg) G1 94 -0.30 in 35 0.34 in
Chicken Road E-I INERTIA 2X (43 deg) G2 94 -0.33 in 26 0.35 in
Roaring Fork 23 deg Skew G1 95 -0.10 in 30 0.20 in
Roaring Fork 23 deg Skew G2 91 -13.70 in 10 12.80 in
Roaring Fork 23 deg Skew G3 92 -0.20 in 8 0.20 in
Roaring Fork E-I LOAD 100% (23 deg) G1 15 0.00 in 79 0.20 in
Roaring Fork E-I LOAD 100% (23 deg) G2 61 -0.04 in 40 0.07 in
Roaring Fork E-I LOAD 100% (23 deg) G3 61 -0.04 in 40 0.07 in
Roaring Fork E-I INERTIA 2X (23 deg) G1 14 -0.01 in 74 0.20 in
Roaring Fork E-I INERTIA 2X (23 deg) G2 18 -0.02 in 46 0.20 in
Roaring Fork E-I INERTIA 2X (23 deg) G3 61 -0.50 in 40 0.08 in
TOTAL DISPLACEMENTS TOP FLANGE
MIN DISPLACEMENT MAX DISPLACEMENT
VALUE VALUE
BRIDGE PARAMETER GIRDER
144
Table 7-6. Summary of LFB Displacements
7.5.2 LFB stresses vs. Torsional displacements.
Throughout the investigation of the LFB stresses on steel skewed bridges it was found,
among other things, that from the total lateral displacements, the values that seem to be
determinant are those coming from the torsional rotations. To verify this condition both the
stress and rotation profiles were compared to determine a possible agreement in the overall
behavior that could confirm the original hypothesis of a torsional controlled phenomenon.
Figure 7-14 shows what is found to be a typical comparison between the LFB stress profile
and the rotation profile.
There can clearly be seen a strong degree of correspondence between them. Both profiles
seem to experience maximum and minimum values within the same regions.
LOC (%) LOC (%)
Chicken Road 43 deg Skew G1 87 -0.18 in 18 0.27 in
Chicken Road 43 deg Skew G2 69 -0.11 in 9 0.06 in
Chicken Road E-I LOAD 100% (43 deg) G1 25 -0.08 in 100 0.09 in
Chicken Road E-I LOAD 100% (43 deg) G2 15 0.00 in 78 0.01 in
Chicken Road E-I INERTIA 2X (43 deg) G1 13 0.00 in 52 0.15 in
Chicken Road E-I INERTIA 2X (43 deg) G2 12 -0.03 in 48 0.12 in
Roaring Fork 23 deg Skew G1 14 -0.02 in 78 0.20 in
Roaring Fork 23 deg Skew G2 20 -0.02 in 47 0.12 in
Roaring Fork 23 deg Skew G3 18 -0.04 in 40 0.07 in
Roaring Fork E-I LOAD 100% (23 deg) G1 14 -0.02 in 80 0.20 in
Roaring Fork E-I LOAD 100% (23 deg) G2 61 -0.04 in 40 0.07 in
Roaring Fork E-I LOAD 100% (23 deg) G3 61 -0.04 in 82 0.06 in
Roaring Fork E-I INERTIA 2X (23 deg) G1 14 -0.01 in 73 0.20 in
Roaring Fork E-I INERTIA 2X (23 deg) G2 19 -0.02 in 46 0.17 in
Roaring Fork E-I INERTIA 2X (23 deg) G3 60 -0.04 in 40 0.07 in
BRIDGE PARAMETER GIRDER
LFB DISPLECEMENTS
MIN DISPLACEMENT MAX DISPLACEMENT
VALUE VALUE
145
Figure 7-14. LFB stresses vs. Rotations on the bottom flange
7.5.3 LFB Stresses vs. Skew Angle
The skew angle has proven to be a paramount parameter as far as the structural behavior of
steel skewed bridges, with the case of LFB stresses being no exception.
Once the stress analysis was finalized on four different skew angles for both bridges, it was
possible to evaluate how relevant the skew angle was on the behavior. Figure 7-15 shows this
situation for Chicken Road Bridge. Likewise, Figure 7-16 depicts the maximum stress values
for Roaring Fork Road Bridge.
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
-50
-40
-30
-20
-10
0
10
20
30
40
50
0 10 20 30 40 50 60 70 80 90 100
RO
TATI
ON
S (d
eg)
F /
Fy (
%)
SPAN (%)
Comparisson between LFB Stresses and Rotations
Cross Frames BOTTOM LEFT BOTTOM RIGHT ROTATIONS
146
Figure 7-15. Maximum stress values for Chicken Road bridge versus skew angle.
Figure 7-16. Maximum stress values for Roaring Fork Road bridge versus skew angle.
0
10
20
30
40
50
60
70
80
90
100
20 30 40 50 60 70 80 90 100
F /
Fy (
%)
SKEW (DEG)
FLEXURAL STRESS RATIOS ON FLANGES
Max Tot on BF Max LFB on BF
Max Tot on TF Max LFB on TF
0
10
20
30
40
50
60
70
80
90
100
20 30 40 50 60 70 80 90 100
F /
Fy (
%)
SKEW (DEG)
FLEXURAL STRESS RATIOS ON FLANGES
Max Tot on BF Max LFB on BF
Max Tot on TF Max LFB on TF
147
It can be clearly noticed from both figures that regardless of the bridge in question, the trend
suggests that as the skew angle is increased the total stress increases while the LFB stresses
decrease. As the values of the skew angle get closer to 90 degrees both behaviors tend to
stabilize.
148
CHAPTER 8. SUMMARY, OBSERVATIONS AND CONCLUSIONS
8.1 General
This section presents a summary of the present investigation and a review of the most
important observations found during this research. In addition, it contains a list of primary
conclusions that were found about torsional rotations of skewed steel plate girder bridges.
8.2 Summary
The primary objectives of the proposed research are to quantify the lateral flange bending of
steel plate girders in heavily skewed bridges, develop a methodology for predicting the
magnitude of lateral translation of the girder flanges due to this effect, and establish
recommended strategies for mitigating the effect of heavy skew.
To achieve these objectives an extensive literature review was carried out on Chapter 2. It
was classified into four major categories, construction issues, parametric studies, steel bridge
studies and NCSU / NCDOT related studies. Some of the most advanced research approaches
and techniques were carefully selected through the literature review stage and adopted to
develop the current limited knowledge.
Chapter 3 summarizes all the steps adopted through the field investigation during the
construction process, including the instrumentation and procedures utilized in order to
validate the numerical techniques required to develop the investigation. Chapter 4 presents
the Finite Element modeling approaches taken to develop a reliable and accurate model that
could serve as a useful tool to characterize the behavior of the steel skewed bridges,
including the model evolution necessary to determine that most suitable approach for the
level of accuracy required.
As a result of the analytical investigation it was possible to identify trends on the bridge
response as far as the transverse rotations. Chapter 5 presents these findings acknowledging
149
that it is possible to predict the response by means of simplified model. Chapter 6 represents
the main analytical phase of the research. A total of eight numerical and four non-numerical
parameters were incorporated. For most of them variations included changes in the parameter
itself combined with changes in the skew angle for the two bridges leading to more than 180
cases studied. In order to simplify the study only cross section torsional rotations were
considered. On the other hand, the response in terms of the lateral flange bending stresses
was studied on Chapter 7. It included a comprehensive investigation aimed to verify and
quantify the overall flexural stresses that take place in the flanges under this condition.
8.3 Outstanding observations
Following will be presented the most important observations related to field measurements
and finite element modeling that were found throughout this investigation
The torsional rotation phenomenon is not random. However, it can be predicted and it
can also be modeled.
The original Finite Element model of the bridge was improved by including and
substituting some of the original types of elements by other more appropriate to the
objective of the investigation.
The final Finite Element model accounted for the effect of parameters that were not
considered on previous investigations such as elastomeric pads, gusset plates, bolts,
etc.
With the exception of the end bents and the vicinity of the crossframes locations, the
girders cross sections behave in a rigid body fashion. The differences in rotation
between flanges and web were less than ten percent, hence they are considered
negligible.
The field measured rotations for Chicken Road Bridge matched the rotations obtained
from the Finite Element Model. However, for Roaring Fork Road Bridge, this
observation cannot be stated with the same degree of certainty due to the site
150
constraints that led to a lack of enough rotation readings along the span of each
girder.
The location of the inflection point along the span can be predicted with relatively
high accuracy. This can be achieved by means of a linear equation that ends up being
a function of the skew angle.
There is substantial scatter for the values of the initial and final rotations as it was for
the initial and final segment slopes, despite mean values showing an almost identical
behavior.
The parametric analysis involved 8 different numerical parameters and 3 geometrical
for at least 3 skew angles on both bridges. These parameters were studied for at least
three different values. All these considerations led to more than 180 different models,
from which the analysis was done.
The parametric analysis for the numerical parameters provided the necessary
information to classify the results into three groups. The first group contains the
unfavorable cases, the second group related to the neutral cases, and the third group
dealt with the favorable cases.
The presence of crossframes on the end bents as well as along the span produces
stress concentrations at the top and bottom flanges.
The total longitudinal stress is a combination of those coming from the web flexure
and those from the LFB.
8.4 Conclusions
After analyzing all the information obtained from the field and the modeling processes, it
was possible to develop the following conclusions:
Most of the forces on the SIP truss model are carried by the diagonals, suggesting a
shear type of force mechanism.
151
At the end bent regions most of the horizontal forces are taken by the end bent
crossframes or diaphragms. For example, on Roaring Fork Road Bridge the factor
was up to six, meaning the forces on the crossframes were six times higher than the
forces on the SIP forms along the span.
The Final model that incorporated the missing SIP‟s and the gusset plates resulted in
a more improved version of the bridge since it accounted for the actual constraints at
the end bents and depicted more accurately the real behavior of the girders.
Deflections can be predicted as a function of the skew angle. It turns out that this
relationship follows a quadratic expression that is unique for each bridge.
On the torsional rotation profile several key points can be identified such as the initial
and final rotations, the inflection point, and the minimum and maximum rotations. It
was concluded that locations of these points along the span are almost skew
independent. These values were found to be approximately 20% span from each end
for the minimum and maximum rotations and near 50% span for the inflection point.
The mid segment slope can be estimated with a linear equation that turns out to be a
function of the skew angle as well.
It was possible to develop a simplified model to predict the torsional rotation values
for a skewed bridge whose skew angles lie within 30 and 75 degrees. Although the
value of 90 degrees was considered at some point in the investigation, as mentioned
on previous sections, its results did not provide information worth being mentioned.
The lower and upper bounds of the simplified model can be determined by
considering amplitude of two standard deviations.
All the parameters selected for the analysis turned out to be skew dependent. Hence,
the effect of the skew could not be isolated from the rest of the parameters,
particularly during the comparison process.
The LFB displacements were found to be negligible when compared to those coming
from the torsional rotations.
152
The unfavorable numerical parameters variations were found to be the increase of
exterior to interior load ratio, decrease in the stiffness of the stay in place metal deck
forms,.
The neutral parameters variations were the number of girders, the increase or
decrease in the stiffness of the stay in place metal deck forms, and either to increase
or to decrease the overall stiffness of the crossframes.
The favorable variations were found to be the increase of either the exterior girders or
the interior girders moments of inertia, increase the number of crossframes, and
increase the number of transverse stiffeners along the span.
The X-type of crossframes yielded the best results as far as controlling the girder‟s
transverse rotations.
Laying the crossframes aligned and perpendicular to the girders produced the highest
forces and as the skew angle changes towards the non skewed condition these forces
tend to decrease regardless of the crossframe layout adopted.
Determining the stresses and rotations from a finite element model that considers
straight girders seems to mach to the stresses and rotations from the cambered
structure. This suggests that to account for the dead load fit, rotations can be predicted
using models with straight girders.
The pouring sequence on which the concrete is cast on the central half of the bridge
produced similar stresses and rotations to those obtained from the full load case,
suggesting it does not enhance the response of the structure.
The disturbed zone on the LFB stress profile is on average along the first 20 percent
of the span at each end of the girder.
The maximum LFB stress found was 18% on the bottom flange whereas the
maximum value observed on the top flange was 8%.
When compared, qualitatively speaking, to the torsional rotations profile, the LFB
stresses showed good agreement. They both seem to experience the same trend, in the
sense that both develop high values in the disturbed regions and low values in the
stable zone.
153
The skew angle proved to be a determinant parameter on the LFB behavior. It was
shown that as it is changed from high values to 90 degrees, the total stresses increase
but the LFB stresses decrease, up to a point that at 90 degrees skew their values are
negligible.
154
CHAPTER 9. RECOMMENDATIONS AND FUTURE WORK
At some point during the investigation it was possible to apply the acquired knowledge onto
another real structure that was still on the design phase. This was the case of the Bridge No
26 over Linville River. This structure was not only modeled using a Finite Element Analysis
but its behavior was also predicted using the proposed simplified methodology. According to
information provided by the NCDOT personnel, the deflections measured at the end bents of
the bridge after the concrete deck was cast indicated that the procedure was able to
successfully predict the deformations on the structure.
This is actual evidence that it is possible to design a steel skewed bridge to fit under dead
load. Even though the investigation did not account for this condition as a parameter to be
studied, the overall result of incorporating all of the structural components during the Finite
Element modeling phase of the investigation combined with the use of the simplified
methodology to determine lateral displacements rendered appropriate results. Hence it is
recommended that besides the potential analytical approach to the problem by means of a
finite element software, a preliminary calculation of the lateral displacements should be
performed to estimate the lateral movement of the girders beforehand, allowing design
engineer to take the necessary actions if required to mitigate any undesired condition that
might arise.
Based on the findings, it is convenient to consider any of the following mitigation strategies
if the structure shows excessive rotations:
Use X-type of crossframes instead of K-type.
Increase, if possible, the torsional stiffness of the exterior girders only, either by using
thicker flanges or thicker webs.
Reduce, if possible, the width of the overhangs.
155
Consider using crossframes laid out perpendicular to the girders and aligned with
each other. Crossframes aligned to the abutments rendered the best results, however
due to the difficulties related to construction and erection for the particular case of
heavily skewed angle bridges, it may be convenient to use the aforementioned
alternative. Nevertheless, other issues like fatigue and stress concentrations must be
studied for this type of crossframe layout on future investigations.
Increase the number of crossframes.
Any combination of the above suggestions.
On the other hand, it is required to incorporate more bridges in future investigations in order
to narrow the range of values in the simplified procedure proposed in this research. Due to
the high scatter associated with part of the investigation, the upper and lower bounds of the
proposed simplified procedure are considerably apart from each other since the standard
deviation reached, in some cases, values close to fifty percent. The case of the LFB stresses
is not different. Although the stress values obtained during the investigation were below
20%, it is still required to improve the degree of accuracy of the range of the stable region as
well as the maximum and minimum LFB stresses such that it could be possible to reliably
predict and establish an adequate criterion for mitigation strategies. Additionally, considering
all the information obtained from the field measurements, it would be reasonable to study the
out of plane rotations and stresses phenomena under more controlled conditions that can only
be provided in a laboratory. Many of the variables involved, such as temperature, humidity,
etc. can be monitored with more precision and accuracy to minimize bias associated with
field conditions.
Finally, the extent of this investigation was limited to simply supported steel bridges and
during the non composite phase of the construction process. However, it is highly
recommended to broaden the scope to continuous bridges, incorporating the effects of the
hardened concrete and temperature in an effort to cover all of the possible scenarios and field
conditions.
156
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164
APPENDICES
165
APPENDIX A-1
ANSYS Model Generation Program Flowchart.
This appendix contains a flow chart outlining the computational program developed using a
Visual Basic 6.0TM
Software platform to automate the model generation for the parametric
analysis of skewed steel plate girder bridges.
This flowchart summarizes all the important steps that were taken in order to develop a
comprehensive computational program to generate the input text files utilized by ANASYS
to create the models. It was developed including many different features such as the
capability of selecting the type of crossframe or diaphragm, the number of girders, the skew
angle, the girder spacing, etc. in such a way that the average time for creating one model
from scratch was 4 minutes.
166
Initial End Bent
Stiffeners
Skew < 90
N<Ngirders
Skew >=90
N>1
Left Connectors
Skew <90
N>1
Left Connectors Right Connectors
no no
yes yes yes
Right Connectors
Skew >=90
N<Ngirdersno
yes
Final End Bent
Stiffeners
SIPSInt(stanq_corr/
LSIP)
End_Bent_
Top_strut_Aux
End_Bent_Top_
Strut<> 0
= 0
N=1 to Ngirders-1
M=1 to 2
Xftype =2,3Top_Strut_Mid_
Gusset_Plateyes
Skew<90
Xftype=2,3
no
Left_b_Gusset_
Plate
Left_t_Gusset_
Plate
N+1
Right_b_Gusset_
Plate
N+1
Right_t_Gusset_
Plate
yes End ifA B
ELASTOMERS
WEBSOLE PLATESOLE PLATE
CONNECTORSTOP FLANGE
BOTTOM
FLANGE
FOR N= 1 TO
NGIRDERSINPUT DATA
PROPERTIESSTART DIM VARIABLES
PROGRAM TO GENERATE THE IMPUT DATA FOR ANSYS
ON SKEWED STEEL GIRDER BRIDGES
FLOWCHART
NEXT N
167
Skew<90
Xftype=1
Left_t_Gusset_
Plate
N+1
Right_t_Gusset_
Plateyes End if
A
Skew >= 90
Xftype=1
no
Skew >= 90
Xftype =2,3
Right_b_Gusset_
Plate
Right_t_Gusset_
Plate
N+1
Left_b_Gusset_
Plate
N+1
Left_t_Gusset_
Plateyes
End if
no
Right_t_Gusset_
Plate
N+1
Left_t_Gusset_
Plateyes End if
B
Xftype =2,3End_bent_
Diagonalsyes
XFtype
Intermediate_
Diaphragms
Intermediate_
Cross_Frames_K
= 1
Intermediate_
Cross_Frames_X= 3
= 2
Int(stanq_corr/
LSIP <> 0Rigid_Connectorsyes
Next Nno
Constrains
Loads
Nodes_and_
Elements_1
Nodes_and_
Elements_2
Output
NEXT N
END
168
APPENDIX A-2
Visual Basic Program used to automate model input data
Overview
By means of Visual Basic 6.0 it was possible to create a computational program to generate
the input data ANSYS uses to analyze the models. The program consists of a series of
modules that logically connect with one another to generate the output text file that can be
processed by ANSYS.
Initially the program needs the input data, represented by the geometrical variables of the
structure, such as span, girder spacing, number of crossframes, skew angle, girder cross
section dimensions, etc. It also requires the material properties to be inputted at the beginning
of the program. In Appendix A the logical flowchart of the program is shown.
Limitations
Some conditions must be satisfied in order to run the program and some variables are limited
to certain values. To list a few:
The structure‟s boundary conditions are pinned and roller connected. No vertical
uplift is allowed.
Do not include typical tapered bottom flanges at the end bents.
All girders must have the same web height.
All intermediate crossframes must be the same type.
Description
Following is a brief description of the Visual Basic 6.0 program.
169
1. The program requires from the user the input of a series of variables. These
variables, as mentioned before, are geometric.
2. Nodes and Elements are generated for the bottom flange, top flange, web, sole
plates, elastomeric pads, and end bent stiffeners (or connectors) on each girder.
3. Connectors and stay in place nodes and elements are then created, followed by the
end bent diaphragms or crossframes and finally the intermediate crossframes.
4. The final step deals with the boundary conditions, constrains, loading scenarios,
and output, which includes the files with deformations and forces data as well as
secondary text files for verification purposes.
The aforementioned steps are just a summary of what the program does. The actual program
included more than 30 different modules and procedures.
170
APPENDIX B
Deflections and rotations Summary for Chicken Road Bridge on
Lumberton, NC.
This appendix contains a detailed description of the Chicken Road Bridge, located in
Lumberton, North Carolina. It includes bridge geometry, material data, crossframe type and
size, and dead loads calculated from slab geometry. Illustrations detailing the bridge
geometry and field measurement locations are included, along with tables and graphs of the
field measured non-composite girder deflections and torsional rotations.
A summary the ANSYS finite element model created for the Chicken Road Bridge is also
included in this appendix. This summary includes a picture of the ANSYS model, details
about the elements used in the model generation, the loads applied to the model, and tables
and graphs of the deflections and torsional rotations predicted by the model.
171
FIELD MEASUREMENTS SUMMARY
PROJECT NUMBER R-513BB (Bridge on Chicken Rd. over US74)
MEASUREMENT DATE
BRIDGE DESCRIPTION
TYPE Two Simple Spans
AVERAGE LENGTH
NUMBER OF GIRDERS 4
GIRDER SPACING
SKEW 137 deg
OVERHANG
(average from web centerline)
BEARING TYPE Elastomeric Bearing
MATERIAL DATA
STRUCTURAL STEEL Grade Yield Strength
Girder AASHTO M270
CONCRETE UNIT WEIGHT
SIP FORM WEIGHT
GIRDER DATA
LENGTH
TOP FLANGE WIDTH 14.17 in
BOTTOM FLANGE WIDTH 18.11 in
WEB THICKNESS 0.63 in
WEB DEPTH 57.09 in
FLANGES Thickness Begin End
Top 0.87 in 00.00 ft
Bottom 0.87 in 00.00 ft
1.57 in 27.53 ft
0.87 in 103.71 ft
STIFFENERS
Longitudinal NONE
Bearing PL 0.87 in x 8.74 in
Intermediate PL 0.87 in x 8.74 in
CROSS FRAME DATA
Type Diagonals Horizontals
END K WT 125 x 22.5 C 380 x 60 @top
WT 125x22.5 @ bottom
INERMEDIATE K L 76 x 76 x 7.9 L 76 x 76 x 7.9
39.99 ft
27.53 ft
103.71 ft
131.20 ft
Tuesday, July 17, 2007
131.20 ft
09.84 ft
130.62 ft 131.00 ft 131.39 ft 131.78 ft
G4
G1 G4
G1 G2 G3
03.26 ft 03.26 ft
50 ksi
145 pcf
3 psf
172
FIELD MEASUREMENTS SUMMARY
PROJECT NUMBER: R-513BB (Bridge on Chicken Rd. over US74)
MEASUREMENT DATE:
SLAB DATA
THICKNESS 8.66 in
lb/ft N/mm lb/ft N/mm BUILD-UP 2.76 in
G1 858 12.54346 724 10.58446 1.19 REBAR Size Spacing
G2 1030 15.05801 827 12.09026 1.25 LONGITUDINAL (metric) (nominal)
G3 1030 15.05801 827 12.09026 1.25 Top #13 16.53 in
G4 858 12.54346 724 10.58446 1.19 Bottom #16 8.66 in
TRANSVERSE
Top #16 5.91 in
Bottom #16 5.91 in
GIRDER DEFLECTIONS
THEORETICAL by SIMP. PROCEDURE (in) MEASURED CORRECTED (in)
(design less slab*) (measured less bearing settlements)
LOCATION G1 G2 G3 G4 LOCATION G1 G2 G3 G4
0/4 0 0 0 0 0/4 0 0 0 0
1/4 -2.76 -2.56 -2.56 -2.76 1/4 -3.36 -3.18 -3.04 -3.14
2/4 -3.74 -3.50 -3.50 -3.74 2/4 -4.86 -4.55 -4.35 -4.52
3/4 -2.76 -2.56 -2.56 -2.76 3/4 -3.42 -3.24 -3.10 -3.14
4/4 0 0 0 0 4/4 0 0 0 0
* Slab includes rebar, build-ups, sip's and girders
GIRDER ROTATIONS
MEASURED
TOP FLANGE @ END BENT (degrees) WEB (degrees)
LOCATION G1 G2 G3 G4 LOCATION G1 G2 G3 G4
0/4 0.9 0.3 0.9 0.5 0/4 0.6 0.6 0.7 0.7
1/4 0.3 1.2 0.7 1.2
BOTTOM FLANGE (degrees) 2/4 -0.5 0.2 0 0.2
3/4 -0.9 -0.4 -0.5 -0.2
LOCATION G1 G2 G3 G4 4/4 -0.6 -0.7 -0.7 -0.5
0/4 -0.6 -0.3 -1.1 -0.5
1/4 0.1 0.3 0.5 0.7
2/4 -1.4 -0.3 0.1 -1
3/4 -1.6 -0.6 -0.8 -0.6
4/4 -0.4 -0.4 0.2 -0.2
Tuesday, July 17, 2007
Concrete Deck SlabRatioGirder
DECK LOADS
173
FIELD MEASUREMENT SUMMARY
PROJECT NUMBER: R-513BB (Bridge on Chicken Rd. over US74)
MEASUREMENT DATE: 7/17/2007
(A) Plan View (not to scale)
(B) Elevation View (not to scale)
DIAL GAUGES
TELLTAIL
G1
G2
G3
G4
Span = 131.2 ft
137 deg
Pour Direction
Survey CL
32.8 ft 32.8 ft 32.8 ft 32.8 ft
ExpansionSupport
FixedSupport
Pavement
Tell -tail
¾ P
oin
t
¼ P
oin
t
Mid
span
Pour DirectionSpan ASpan B
174
Plan and Elevation View of Chicken Road Bridge
FIELD MEASUREMENT SUMMARY
PROJECT NUMBER: R-513BB (Bridge on Chicken Rd. over US74)
MEASUREMENT DATE: 7/17/2007
-5
-4
-3
-2
-1
0
0/4 1/4 2/4 3/4 4/4
De
fle
ctio
ns
(in
)
SPAN LOCATION
SIMPLIFIED PROCEDURE
G1 G2 G3 G4
-5
-4
-3
-2
-1
0
0/4 1/4 2/4 3/4 4/4
De
fle
ctio
ns
(in
)
SPAN LOCATION
MEASURED
G1 G2 G3 G4
-1.5
-1
-0.5
0
0.5
1
1.5
0/4 1/4 2/4 3/4 4/4
RO
TATI
ON
S (d
eg)
SPAN LOCATION
Field Rotations
G1 G2 G3 G4
175
FIELD MEASUREMENT SUMMARY
PROJECT NUMBER: R-513BB (Bridge on Chicken Rd. over US74)
MEASUREMENT DATE: 7/17/2007
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
G1 G2 G3 G4D
EFLE
CTI
ON
S (i
n)
GIRDERS
Deflections at 1/4 of Span A
MEASURED THEORETICAL
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
G1 G2 G3 G4
DEF
LEC
TIO
NS
(in
)
GIRDERS
Deflections at Midspan A
MEASURED THEORETICAL
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
G1 G2 G3 G4
DEF
LEC
TIO
NS
(in
)
GIRDERS
Deflections at 3/4 of Span A
MEASURED THEORETICAL
176
ANSYS FINITE ELEMENT MODELING SUMMARY
PROJECT NUMBER: R-513BB (Bridge on Chicken Rd. over US74)
MODEL DESCRIPTION: Steel Only, Isometric View
G4
G3
G2
G1
177
ANSYS FINITE ELEMENT MODELING SUMMARY
PROJECT NUMBER: R-513BB (Bridge on Chicken Rd. over US74)
MODEL DESCRIPTION: Steel Only, Isometric View
COMPONENT ELEMENT TYPE
Girder: SHELL 93 lb/ft2 N/mm2
Connector/ Stiffener Plates: SHELL 93 G1 1.34 0.064
Cross Frame Members: Link 8 (Diagonal) G2 1.57 0.075
Link 8 (Horizontal) G3 1.57 0.075
End Diaphragm Link 8 (Diagonal) G4 1.34 0.064
Beam 4 (Horizontal)
Stay in Place Deck Forms Link 8
GIRDER DEFLECTIONS (in) GIRDER ROTATIONS
(@ COMMON NODE BETWEEN BOTTOM FLANGE AND WEB) WEB (degrees)
LOCATION G1 G2 G3 G4 LOCATION G1 G2 G3 G4
0/4 -0.00982 -0.01142 -0.01159 -0.01255 0/4 0.1 0.3 0.3 0.3
1/4 -6.30 -6.21 -6.24 -6.52 1/4 0.9 0.8 0.6 0.4
2/4 -9.02 -8.71 -8.70 -8.99 2/4 0.3 0.1 -0.1 -0.3
3/4 -6.55 -6.24 -6.20 -6.29 3/4 -0.4 -0.6 -0.8 -0.9
4/4 -0.00576 -0.00532 -0.0054 -0.00406 4/4 -0.3 -0.3 -0.3 -0.1
LoadGirder
-10
-8
-6
-4
-2
0
0/4 1/4 2/4 3/4 4/4
DEF
LEC
TIO
NS
(in
)
LOCATION
ANSYS TOTAL DEFLECTIONS
G1 G2 G3 G4
-1.0
-0.5
0.0
0.5
1.0
0/4 1/4 2/4 3/4 4/4
RO
TATI
ON
S (d
eg)
LOCATION
ANSYS TORSIONAL ROTATIONS
G1 G2
G3 G4
178
APPENDIX C
Deflections and rotations Summary for Roaring Fork Road Bridge near
Jefferson, ASHE County, NC.
This appendix contains a detailed description of the Roaring Fork Road Bridge, located near
Jefferson, North Carolina. It includes bridge geometry, material data, crossframe type and
size, and dead loads calculated from slab geometry. Illustrations detailing the bridge
geometry and field measurement locations are included, along with tables and graphs of the
field measured non-composite girder deflections and torsional rotations.
A summary of the ANSYS finite element model created for the Raring Fork Road Bridge is
also included in this appendix. This summary includes a picture of the ANSYS model, details
about the elements used in the model generation, the loads applied to the model, and tables
and graphs of the deflections and torsional rotations predicted by the model.
179
FIELD MEASUREMENTS SUMMARY
PROJECT NUMBER B-4013 (Bridge No. 338 over Roaring Fork Creek)
MEASUREMENT DATE
BRIDGE DESCRIPTION
TYPE Simple Span
AVERAGE LENGTH
NUMBER OF GIRDERS 5
GIRDER SPACING
SKEW 23 deg
OVERHANG
BEARING TYPE Elastomeric Bearing
MATERIAL DATA
STRUCTURAL STEEL Grade Yield Strength
Girder AASHTO M270
CONCRETE UNIT WEIGHT
SIP FORM WEIGHT CAT#: 30B156-20-G1BB
GIRDER DATA
LENGTH G1 G2
Bearing to Bearing 73.50 ft 73.50 ft
TOTAL 74.50 ft 74.50 ft
TOP FLANGE WIDTH 12.00 in
TOP FLANGE THICKNESS 0.75 in
BOTTOM FLANGE WIDTH 18.00 in
BOTTOM FLANGE THICKNESS 1.00 in
WEB THICKNESS 0.50 in
WEB DEPTH 32.00 in
STIFFENERS
Longitudinal NONE
Bearing PL 0.75 in x 5.75 in
Intermediate PL 0.5 in x 5.75 in
CROSS FRAME DATA
Type Section
END DIAPHRAGM MC 18 x 42.5
INERMEDIATE DIAPHRAGM MC 18 x 42.5
74.50 ft
Thursday, March 06, 2008
G5
73.50 ft 73.50 ft 73.50 ft
50 ksi
145 pcf
3 psf
74.50 ft
6.50 ft
G1 G5
1.10 ft 1.10 ft
G3 G4
74.50 ft 74.50 ft
180
FIELD MEASUREMENTS SUMMARY
PROJECT NUMBER: B-4013 (Bridge No. 338 over Roaring Fork Creek)
MEASUREMENT DATE:
DECK LOADS SLAB DATA
THICKNESS 8.0 in
lb/ft N/mm lb/ft N/mm BUILD-UP 2.5 in
G1 492 7.19 637 9.31 0.77 REINFORCEMENT Size Spacing
G2 731 10.69 946 13.83 0.77 LONGITUDINAL (metric) (nominal)
G3 731 10.69 946 13.83 0.77 Top #4 18.0 in
G4 731 10.69 946 13.83 0.77 Bottom #5 12.0 in
G5 492 7.19 637 9.31 0.77 TRANSVERSE
Top #5 8.0 in
Bottom #5 8.0 in
GIRDER DEFLECTIONS
THEORETICAL by SIMP. PROCEDURE (in)
(design less slab*)
LOCATION G1 G2 G3 G4 G5
MIDSPAN N/A N/A N/A N/A N/A
* Slab includes rebar, build-ups, sip's and girders
Note: the parameter S (Girder spacing to span ratio) on the simplified procedure
was out of bounds, so it was not possible to determine the deflections
MEASURED CORRECTED (in)
(measured less bearing settlements)
LOCATION G1 G2 G3 G4 G5
MIDSPAN -1.22 -1.20 -1.22 -1.27 -1.42
GIRDER ROTATIONS
MEASURED
BOTTOM FLANGE (degrees)
LOCATION G1 G2 G3 G4 G5
END BENT 1 0.6 0.1 0 0.1 -0.7
MIDSPAN -0.3 0.4 0.3 0.1 -0.3
END BENT 2 -0.9 -0.9 -0.8 -0.3 -0.1
WEB (degrees)
LOCATION G1 G2 G3 G4 G5
END BENT 1 -0.1 -0.2 -0.3 -0.4 0
MIDSPAN -0.3 -0.4 0 0.2 0.2
END BENT 2 0.7 1 0.4 0.9 0.1
GirderConcrete Deck Slab
Thursday, March 06, 2008
Ratio
181
FIELD MEASUREMENT SUMMARY
PROJECT NUMBER: B-4013 (Bridge No. 338 over Roaring Fork Creek)
MEASUREMENT DATE: 3/6/2008
(C) Plan View (not to scale)
(D) Elevation View (not to scale)
G1
G2
G3 G3
G4
G5
PourDirection
Survey CL
42’ 6’’
85’
23 deg
STRAIN TRANSDUCERS
STRING POTS
DIAL GAUGES
FixedSupport
Plank String pots
Mid
spa
n
Pour Direction
ExpansionSupport
Creek
182
FIELD MEASUREMENT SUMMARY
PROJECT NUMBER: B-4013 (Bridge No. 338 over Roaring Fork Creek)
MEASUREMENT DATE: 3/6/2008
-1.45
-1.40
-1.35
-1.30
-1.25
-1.20
-1.15
-1.10
-1.05
G1 G2 G3 G4 G5
DEF
LEC
TIO
NS
(in
)
GIRDER
FIELD DEFLECTIONS AT MIDSPAN
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
1.2
END BENT 1 MIDSPAN END BENT 2
RO
TATI
ON
S (d
eg)
SPAN LOCATION
FIELD ROTATIONS
G1 G2 G3 G4 G5
183
ANSYS FINITE ELEMENT MODELING SUMMARY
PROJECT NUMBER: B-4013 (Bridge No. 338 over Roaring Fork Creek)
MODEL DESCRIPTION: Steel Only, Isometric View
G1
G2
G3
G4
G5
184
ANSYS FINITE ELEMENT MODELING SUMMARY
PROJECT NUMBER: B-4013 (Bridge No. 338 over Roaring Fork Creek)
MODEL DESCRIPTION: Steel Only, Isometric View
COMPONENT ELEMENT TYPE
Girder: SHELL 93 lb/ft2 N/mm2
Connector/ Stiffener Plates: SHELL 93 G1 492.0 0.023
Cross Frame Members: Beam 4 G2 731.0 0.035
End Diaphragm Beam 4 G3 731.0 0.035
Stay in Place Deck Forms Link 8 G4 731.0 0.035
G5 492.0 0.023
GIRDER DEFLECTIONS (in) GIRDER ROTATIONS
(@ COMMON NODE BETWEEN BOTTOM FLANGE AND WEB) WEB (degrees)
LOCATION G1 G2 G3 G4 G5 LOCATION G1 G2 G3 G4 G5
0/4 0.00 0.00 0.00 0.00 0.00 0/4 0.0 -0.1 -0.1 -0.1 -0.1
1/4 -1.02 -1.06 -1.05 -1.05 -1.13 1/4 -0.50 -0.55 -0.53 -0.50 -0.19
2/4 -1.54 -1.51 -1.50 -1.50 -1.53 2/4 -0.34 -0.08 0.00 0.08 0.31
3/4 -1.15 -1.07 -1.06 -1.07 -1.03 3/4 0.26 0.51 0.53 0.55 0.51
4/4 0.00 0.00 0.00 0.00 0.00 4/4 0.05 0.08 0.09 0.07 0.01
GirderLoad
-1.80
-1.60
-1.40
-1.20
-1.00
-0.80
-0.60
-0.40
-0.20
0.00
0/4 1/4 2/4 3/4 4/4
DEF
LEC
TIO
NS
(in
)
LOCATION
ANSYS TOTAL DEFLECTIONS
G1 G2 G3 G4 G5
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
0/4 1/4 2/4 3/4 4/4
RO
TATI
ON
S (d
eg)
LOCATION
ANSYS TORSIONAL ROTATIONS
G1 G2 G3 G4 G5
185
APPENDIX D
Lateral Flange Bending Displacements for Chicken Road Bridge and
Roaring Fork Bridge
186
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NONE
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
187
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NONE
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
188
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NONE
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
189
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NONE
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
190
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NONE
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
191
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NONE
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
192
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 0.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
193
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 0.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
194
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 2.0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
195
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 2.0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
196
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 0.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
197
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 0.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
198
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 2.0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
199
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 2.0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
200
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 0.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
201
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 0.5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
202
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 2.0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
203
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR GIRDER MOMENT OF INERTIA RATIO OF 2.0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
204
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 50%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
205
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 50%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
206
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 100%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
207
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 100%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
208
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 50%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
209
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 50%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
210
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 100%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
211
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 100%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
212
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 50%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
213
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 50%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
214
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 100%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
215
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: EXTERIOR TO INTERIOR LOAD RATIO OF 100%
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
216
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
217
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
218
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
219
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
220
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G3 SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
221
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
222
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
223
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G3 SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
224
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G4 SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
225
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
226
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
227
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
228
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
229
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G3 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
230
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
231
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
232
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G3 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
233
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G4 SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
234
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
235
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N-1
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
236
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
237
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
238
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G3 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N+2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
239
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR G1 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
240
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G2 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
241
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G3 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
242
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR G4 SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF GIRDERS = N+5
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
243
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF STIFFENERS = 1.83X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
244
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF STIFFENERS = 1.83X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
245
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF STIFFENERS = 2.33X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
246
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF STIFFENERS = 2.33X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
247
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF STIFFENERS = 1.83X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
248
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF STIFFENERS = 1.83X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
249
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF STIFFENERS = 2.33X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
250
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF STIFFENERS = 2.33X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
251
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF STIFFENERS = 1.83X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
252
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF STIFFENERS = 1.83X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
253
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF STIFFENERS = 2.33X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
254
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF STIFFENERS = 2.33X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
255
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
256
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
257
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 2X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
258
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 2X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
259
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
260
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
261
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 2X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
262
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 2X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
263
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
264
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
265
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 2X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
266
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NUMBER OF CROSSFRAMES = 2X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
267
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 0.1X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
268
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 0.1X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
269
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 10X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
270
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 10X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
271
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 0.1X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
272
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 0.1X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
273
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 10X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
274
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 10X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
275
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 0.1X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
276
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 0.1X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
277
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 10X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
278
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SIP’S AXIAL STIFFNES = 10X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
279
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SPACE TO SPAN RATIO = 0.5X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
280
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SPACE TO SPAN RATIO = 0.5X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
281
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SPACE TO SPAN RATIO = 1.25X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
282
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: SPACE TO SPAN RATIO = 1.25X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
283
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SPACE TO SPAN RATIO = 0.5X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
284
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SPACE TO SPAN RATIO = 0.5X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
285
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SPACE TO SPAN RATIO = 1.25X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
286
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SPACE TO SPAN RATIO = 1.25X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
287
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SPACE TO SPAN RATIO = 2.0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
288
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: SPACE TO SPAN RATIO = 2.0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
289
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SPACE TO SPAN RATIO = 0.5X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
290
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SPACE TO SPAN RATIO = 0.5X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
291
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SPACE TO SPAN RATIO = 1.25X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
292
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SPACE TO SPAN RATIO = 1.25X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
293
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SPACE TO SPAN RATIO = 2.0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
294
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: SPACE TO SPAN RATIO = 2.0X
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
295
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 0.5A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
296
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 0.5A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
297
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 2.0A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
298
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 2.0A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
299
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 0.5A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
300
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 0.5A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
301
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 2.0A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
302
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 2.0A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
303
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 0.5A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
304
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 0.5A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
305
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 2.0A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
306
NORMALIZED LATERAL FLANGE BENDING DISPLACEMENTS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAMES STIFFNESS 2.0A
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENT
SPAN (%)
Normalized Lateral Flange Bending Displacements on Bottom Flange
Norm Total Norm due to Rotation Norm LFB
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
NO
RM
ALI
ZED
DIS
PLA
CEM
ENTS
SPAN (%)
Normalized Lateral Flange Bending Displacements on Top Flange
Norm Total Norm due to Rotation Norm LFB
307
APPENDIX E
Lateral Flange Bending Stresses for Roaring Fork Bridge.
308
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
309
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
0 10 20 30 40 50 60 70 80 90 100
F/Fy
(%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
G1G3
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F/Fy
(%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
G1G3
310
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: CENTRAL SKEW ANGLE: 23 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G3
TOP RIGHT TOP LEFT
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G3
BOTTOM RIGHT BOTTOM LEFT
311
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
312
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
313
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: CENTRAL SKEW ANGLE: 45 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G3
TOP RIGHT TOP LEFT
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G3
BOTTOM RIGHT BOTTOM LEFT
314
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
315
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
316
NORMALIZED LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: CENTRAL SKEW ANGLE: 75 DEGREES PARAMETER: NONE
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON TOP FLANGE OF G3
TOP RIGHT TOP LEFT
-40
-30
-20
-10
0
10
20
30
40
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G3
BOTTOM RIGHT BOTTOM LEFT
317
APPENDIX F
Lateral Flange Bending Stresses and Rotations on Chicken Road Bridge
and Roaring Fork Road Bridge for the Crossframe Layout condition.
318
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
319
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
320
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
321
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
322
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
323
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
324
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 25 DEGREE SKEW ANGLE
25 DEGREES PARALLEL
25 DEGREES ORIGINAL
25 DEGREES DIFFERENCE
325
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 25 DEGREE SKEW ANGLE
25 DEGREES X-TYPE
25 DEGREES ORIGINAL
25 DEGREES DIFFERENCE
326
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 43 DEGREE SKEW ANGLE
43 DEGREE PARALLEL
43 DEGREE ORIGINAL
43 DEGREE DIFFERENCE
327
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 43 DEGREE SKEW ANGLE
43 DEGREE X-TYPE
43 DEGREE ORIGINAL
43 DEGREE DIFFERENCE
328
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 75 DEGREE SKEW ANGLE
75 DEGREE PARALLEL
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
329
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 75 DEGREE SKEW ANGLE
75 DEGREE X-TYPE
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
330
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
331
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
332
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
333
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
334
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
335
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
336
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 23 DEGREE SKEW ANGLE
23 DEGREES PARALLEL
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
337
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 23 DEGREE SKEW ANGLE
23 DEGREES PARALLEL
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
338
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 45 DEGREE SKEW ANGLE
45 DEGREE PARALLEL
45 DEGREE ORIGINAL
45 DEGREE DIFFERENCE
339
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 45 DEGREE SKEW ANGLE
45 DEGREE PARALLEL
45 DEGREE ORIGINAL
45 DEGREE DIFFERENCE
340
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 75 DEGREE SKEW ANGLE
75 DEGREE PARALLEL
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
341
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 75 DEGREE SKEW ANGLE
75 DEGREE PARALLEL
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
342
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
343
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
344
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
345
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
346
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
347
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
348
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 25 DEGREE SKEW ANGLE
25 DEGREES PERPENDICULAR
25 DEGREES ORIGINAL
25 DEGREES DIFFERENCE
349
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 25 DEGREE SKEW ANGLE
25 DEGREES PERPENDICULAR
25 DEGREES ORIGINAL
25 DEGREES DIFFERENCE
350
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 43 DEGREE SKEW ANGLE
43 DEGREE PERPENDICULAR
43 DEGREE ORIGINAL
43 DEGREE DIFFERENCE
351
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 43 DEGREE SKEW ANGLE
43 DEGREE PERPENDICULAR
43 DEGREE ORIGINAL
43 DEGREE DIFFERENCE
352
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 75 DEGREE SKEW ANGLE
75 DEGREE PERPENDICULAR
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
353
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PERPENDICULAR
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 75 DEGREE SKEW ANGLE
75 DEGREE PERPENDICULAR
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
354
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
355
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
356
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
357
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
358
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
359
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
360
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 23 DEGREE SKEW ANGLE
23 DEGREES PERPENDICULAR
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
361
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 23 DEGREE SKEW ANGLE
23 DEGREES PERPENDICULAR
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
362
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 45 DEGREE SKEW ANGLE
45 DEGREE PERPENDICULAR
45 DEGREE ORIGINAL
45 DEGREE DIFFERENCE
363
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 45 DEGREE SKEW ANGLE
45 DEGREE PERPENDICULAR
45 DEGREE ORIGINAL
45 DEGREE DIFFERENCE
364
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 75 DEGREE SKEW ANGLE
75 DEGREE PERPENDICULAR
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
365
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME LAYOUT - CROSSFRAME PARALLEL
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 75 DEGREE SKEW ANGLE
75 DEGREE PERPENDICULAR
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
366
APPENDIX G
Lateral Flange Bending Stresses and Rotations on Roaring Fork Bridge for
the Dead Load Fit condition.
367
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
368
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
369
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
370
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
371
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
372
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
373
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 90 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
374
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 90 DEGREES PARAMETER: DEAD LOAD FIT
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
375
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: DEAD LOAD FIT
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 23 DEGREE SKEW ANGLE
23 DEGREES CAMBERED
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
376
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: DEAD LOAD FIT
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 23 DEGREE SKEW ANGLE
23 DEGREES CAMBERED
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
377
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: DEAD LOAD FIT
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 45 DEGREE SKEW ANGLE
45 DEGREES CAMBERED
45 DEGREES ORIGINAL
45 DEGREES DIFFERENCE
378
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: DEAD LOAD FIT
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 45 DEGREE SKEW ANGLE
45 CAMB
45 ORIG
45 DIFF
379
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: DEAD LOAD FIT
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 75 DEGREE SKEW ANGLE
75 CAMB
75 ORIG
75 DIFF
380
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: DEAD LOAD FIT
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 75 DEGREE SKEW ANGLE
75 CAMB
75 ORIG
75 DIFF
381
APPENDIX H
Lateral Flange Bending Stresses and Rotations on Roaring Fork Bridge for
the Pouring Sequence of 50% Load condition.
382
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
383
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
384
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
385
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
386
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
387
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
388
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 90 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
389
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 90 DEGREES PARAMETER: POURING SEQUENCE
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
TOPLEFT
TOPRIGHT
TOPMID
EXTERIORINTERIOR
-10
-8
-6
-4
-2
0
2
4
6
8
10
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
BOTTOMLEFT
BOTTOMRIGHT
BOTTOMMID
EXTERIORINTERIOR
390
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: POURING SEQUENCE
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 23 DEGREE SKEW ANGLE
23 DEGREES 50% LOAD
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
391
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 23 DEGREES PARAMETER: POURING SEQUENCE
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 23 DEGREE SKEW ANGLE
23 DEGREES 50% LOAD
23 DEGREES ORIGINAL
23 DEGREES DIFFERENCE
392
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: POURING SEQUENCE
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 45 DEGREE SKEW ANGLE
45 DEGREES 50% LOAD
45 DEGREES ORIGINAL
45 DEGREES DIFFERENCE
393
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 45 DEGREES PARAMETER: POURING SEQUENCE
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 45 DEGREE SKEW ANGLE
45 DEGREES 50% LOAD
45 DEGREES ORIGINAL
45 DEGREES DIFFERENCE
394
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: POURING SEQUENCE
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 75 DEGREE SKEW ANGLE
75 DEGREES 50% LOAD
75 ORIGINAL
75 DEGREES DIFFERENCE
395
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: ROARING FORK GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: POURING SEQUENCE
-20
-15
-10
-5
0
5
10
15
20
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 75 DEGREE SKEW ANGLE
75 DEGREES 50% LOAD
75 DEGREES ORIGINAL
75 DEGREES DIFFERENCE
396
APPENDIX I
Lateral Flange Bending Stresses and Rotations on Chicken Road Bridge
for the Crossframe X-Type condition.
397
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME X-TYPE
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
398
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME X-TYPE
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
399
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME X-TYPE
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
400
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME X-TYPE
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
401
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME X-TYPE
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G1
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G1
BOTTOM RIGHT BOTTOM LEFT
402
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING STRESSES FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME X-TYPE
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON TOP FLANGE OF G2
TOP RIGHT TOP LEFT
-20
-15
-10
-5
0
5
10
15
20
0 10 20 30 40 50 60 70 80 90 100F /
Fy (
%)
SPAN (%)
DIFFERENCE OF LATERAL BENDING STRESSES ON BOTTOM FLANGE OF G2
BOTTOM RIGHT BOTTOM LEFT
403
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME X-TYPE
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 25 DEGREE SKEW ANGLE
25 DEGREES X-TYPE
25 DEGREES ORIGINAL
25 DEGREES DIFFERENCE
404
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 25 DEGREES PARAMETER: CROSSFRAME X-TYPE
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
(%)
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 25 DEGREE SKEW ANGLE
25 DEGREES X-TYPE
25 DEGREES ORIGINAL
25 DEGREES DIFFERENCE
405
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME X-TYPE
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 43 DEGREE SKEW ANGLE
43 DEGREE X-TYPE
43 DEGREE ORIGINAL
43 DEGREE DIFFERENCE
406
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 43 DEGREES PARAMETER: CROSSFRAME X-TYPE
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 43 DEGREE SKEW ANGLE
43 DEGREE X-TYPE
43 DEGREE ORIGINAL
43 DEGREE DIFFERENCE
407
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: EXTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME X-TYPE
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 1 FOR 75 DEGREE SKEW ANGLE
75 DEGREE X-TYPE
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
408
NORMALIZED DIFFERENCE IN LATERAL FLANGE BENDING ROTATIONS FOR:
BRIDGE: CHICKEN ROAD GIRDER: INTERIOR SKEW ANGLE: 75 DEGREES PARAMETER: CROSSFRAME X-TYPE
-500
-400
-300
-200
-100
0
100
200
300
400
500
0.00 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00
RO
T /
RO
T 9
0 D
EGR
EES
SPAN (%)
NORMALIZED ROTATIONS ON GIRDER 2 FOR 75 DEGREE SKEW ANGLE
75 DEGREE X-TYPE
75 DEGREE ORIGINAL
75 DEGREE DIFFERENCE
